002779085 001__ 2779085
002779085 005__ 20241122073554.0
002779085 0248_ $$aoai:cds.cern.ch:2779085$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002779085 0247_ $$2DOI$$9arXiv$$a10.1007/JHEP09(2022)116$$qpublication
002779085 037__ $$9arXiv$$aarXiv:2108.09299$$chep-ph
002779085 037__ $$9arXiv:reportnumber$$aUMN-TH-4023/21
002779085 037__ $$9arXiv:reportnumber$$aFTPI-MINN-21-15
002779085 037__ $$9arXiv:reportnumber$$aCERN-TH-2021-124
002779085 035__ $$9arXiv$$aoai:arXiv.org:2108.09299
002779085 035__ $$9Inspire$$aoai:inspirehep.net:1908426$$d2024-11-21T04:09:17Z$$h2024-11-22T03:00:14Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002779085 035__ $$9Inspire$$a1908426
002779085 041__ $$aeng
002779085 100__ $$aCo, Raymond T.$$jORCID:0000-0002-8395-7056$$tGRID:grid.17635.36$$uMinnesota U., Theor. Phys. Inst.$$vWilliam I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, 55455 Minneapolis, MN, USA
002779085 245__ $$9Springer$$aGravitational Wave and CMB Probes of Axion Kination
002779085 269__ $$c2021-08-20
002779085 260__ $$c2022-09-15
002779085 300__ $$a63 p
002779085 500__ $$9arXiv$$a63 pages, 17 figures; v2: references and discussions added; v3:
matches journal version; v4: journal references updated
002779085 520__ $$9Springer$$aRotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.
002779085 520__ $$9arXiv$$aRotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.
002779085 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002779085 540__ $$3publication$$aCC-BY-4.0$$bSpringer$$fSCOAP3$$uhttp://creativecommons.org/licenses/by/4.0/
002779085 542__ $$3publication$$dThe Authors$$g2022
002779085 595__ $$aCERN-TH
002779085 65017 $$2SzGeCERN$$aAstrophysics and Astronomy
002779085 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002779085 690C_ $$aCERN
002779085 690C_ $$aARTICLE
002779085 700__ $$aDunsky, David$$tGRID:grid.47840.3f$$tGRID:grid.184769.5$$uUC, Berkeley$$uLBL, Berkeley$$vDepartment of Physics, University of California, 94720 Berkeley, CA, USA$$vTheoretical Physics Group, Lawrence Berkeley National Laboratory, 94720 Berkeley, CA, USA
002779085 700__ $$aFernandez, Nicolas$$tGRID:grid.35403.31$$uIllinois U., Urbana$$vDepartment of Physics, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA$$vIllinois Center for Advanced Studies of the Universe, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA
002779085 700__ $$aGhalsasi, Akshay$$tGRID:grid.21925.3d$$uPittsburgh U.$$vPittsburgh Particle Physics, Astrophysics, and Cosmology Center, Department of Physics and Astronomy, University of Pittsburgh, 15260 Pittsburgh, PA, USA
002779085 700__ $$aHall, Lawrence J.$$tGRID:grid.47840.3f$$tGRID:grid.184769.5$$uUC, Berkeley$$uLBL, Berkeley$$vDepartment of Physics, University of California, 94720 Berkeley, CA, USA$$vTheoretical Physics Group, Lawrence Berkeley National Laboratory, 94720 Berkeley, CA, USA
002779085 700__ $$aHarigaya, Keisuke$$tGRID:grid.9132.9$$tGRID:grid.78989.37$$uCERN$$uPrinceton, Inst. Advanced Study$$vTheoretical Physics Department, CERN, Geneva, Switzerland$$vSchool of Natural Sciences, Institute for Advanced Study, 08540 Princeton, NJ, USA
002779085 700__ $$aShelton, Jessie$$tGRID:grid.35403.31$$uIllinois U., Urbana$$vDepartment of Physics, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA$$vIllinois Center for Advanced Studies of the Universe, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA
002779085 773__ $$c116$$pJHEP$$v2209$$y2022
002779085 8564_ $$82317803$$s92599$$uhttps://cds.cern.ch/record/2779085/files/fig_lateKD_NANOGrav.png$$y00028 Left: Required $G\mu$ for $\Omega_{\rm GW}h^2$ to pass through the NANOGrav signal~\cite{NANOGrav:2020bcs,Blasi:2020mfx, Ellis:2020ena}. For long kination eras, which occur when $T_{\rm RM} \gg T_{\rm KR}$, $G\mu$ decreases with respect to the standard $\Lambda$CDM cosmology so that the kination peak does not exceed the NANOGrav signal. Right : The parameter region of axion kination whose imprints on the gravitational wave spectrum from cosmic strings can be detected. For each ($T_{\rm RM},T_{\rm KR})$, we fix $G\mu$ according to the left panel so that spectrum passes through the NANOGrav signal. For the reference $\Lambda$CDM cosmology, we fix $G\mu$ and $\alpha$ to $6 \times 10^{-11}$ and $0.1$, respectively, to also fit NANOGrav. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve of the detector.
002779085 8564_ $$82317804$$s67356$$uhttps://cds.cern.ch/record/2779085/files/fig_TKR10MeV.png$$y00008 The unshaded regions show the allowed parameter space for axion kination for the fixed values of $T_{\rm KR}$ labeled in each panel. Contours of $T_{\rm MK}$ are shown in these regions with kination. The excluded shaded regions are discussed in the text. To achieve minimal ALPgenesis, the parameter space collapses into $m_S \simeq 5 \keV (0.1/c_B)$ as shown by the black solid line in the upper-right panel, or into $f_a$ given by Eq.~(\ref{eq:TKRALPgen}) with $S(T_{\rm ws}) = f_a$ as shown by the black solid line in the lower-right panel, where we take $c_B=0.1$. On the other hand, lepto-ALPgenesis restricts the parameter space to $m_S \gtrsim 30 \TeV$. The axion cannot constitute dark matter via kinetic misalignment in the upper panels due to the warmness constraint in Eq.~(\ref{eq:T_NR}).
002779085 8564_ $$82317805$$s27849$$uhttps://cds.cern.ch/record/2779085/files/fig_axionKD2.png$$y00006 Axion dark matter and the baryon asymmetry from axion rotation. Left panel: in the axion parameter space, contours of $T_{\rm KR} = 1 \GeV$ ($1 \TeV$) are shown in dashed (dot-dashed) lines as predicted by dark matter from kinetic misalignment (purple) and for the baryon asymmetry from minimal ALPgenesis (blue). The contours intersect along the green line where dark matter and the baryon asymmetry are simultaneously explained as in ALP cogenesis. Right panel: the purple lines are the contours of the mass of axion dark matter predicted by kinetic misalignment as a function of $f_a$ and $T_{\rm KR}$. In both panels, the red region is excluded by the warmness of axion dark matter from kinetic misalignment. The yellow line in either plot shows the prediction assuming a QCD axion which terminates at $f_{a} = 10^{8} \GeV $ since lower $f_{a}$ is disfavored by astrophysical constraints.
002779085 8564_ $$82317806$$s63398$$uhttps://cds.cern.ch/record/2779085/files/fig_axionKD1.png$$y00005 Axion dark matter and the baryon asymmetry from axion rotation. Left panel: in the axion parameter space, contours of $T_{\rm KR} = 1 \GeV$ ($1 \TeV$) are shown in dashed (dot-dashed) lines as predicted by dark matter from kinetic misalignment (purple) and for the baryon asymmetry from minimal ALPgenesis (blue). The contours intersect along the green line where dark matter and the baryon asymmetry are simultaneously explained as in ALP cogenesis. Right panel: the purple lines are the contours of the mass of axion dark matter predicted by kinetic misalignment as a function of $f_a$ and $T_{\rm KR}$. In both panels, the red region is excluded by the warmness of axion dark matter from kinetic misalignment. The yellow line in either plot shows the prediction assuming a QCD axion which terminates at $f_{a} = 10^{8} \GeV $ since lower $f_{a}$ is disfavored by astrophysical constraints.
002779085 8564_ $$82317807$$s101273$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis2.png$$y00021 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) wi
002779085 8564_ $$82317808$$s61747$$uhttps://cds.cern.ch/record/2779085/files/fig_SGW_lateKD.png$$y00027 Representative spectra of primordial gravitational waves emitted from local cosmic strings experiencing axion kination (solid) and the standard $\Lambda$CDM cosmology (dashed). Long eras of kination exhibit greater amplitudes in the triangular shaped peak of $\Omega_{\rm GW}h^2$, which is a key signature of axion kination. Of crucial importance is the slowly decaying high frequency tail arising from the sum over high mode numbers which enables detectors like BBO, DECIGO, and CE to detect deviations from the $\Lambda$CDM spectrum even when the kination peak is not located within their frequency domain. Left: Early axion kination cosmology where kination occurs before BBN. The top most contour shows the gravitational wave amplitude when $G\mu$ is fixed to pass through the NANOGrav signal. Right: Late axion kination cosmology where kination occurs in the epoch between CMB and BBN. For each contour, we plot the required $G\mu$ to pass through the NANOGrav signal.
002779085 8564_ $$82317809$$s45385$$uhttps://cds.cern.ch/record/2779085/files/Corner_LCDM_Kination_parameters.png$$y00035 Corner plot for the posterior distributions for the calculated values $\Lambda$CDM parameters and axion kination cosmology. Contours contain 68\% and 95\% of the probability.
002779085 8564_ $$82317810$$s55579$$uhttps://cds.cern.ch/record/2779085/files/fig_TKR150eV.png$$y00007 The unshaded regions show the allowed parameter space for axion kination for the fixed values of $T_{\rm KR}$ labeled in each panel. Contours of $T_{\rm MK}$ are shown in these regions with kination. The excluded shaded regions are discussed in the text. To achieve minimal ALPgenesis, the parameter space collapses into $m_S \simeq 5 \keV (0.1/c_B)$ as shown by the black solid line in the upper-right panel, or into $f_a$ given by Eq.~(\ref{eq:TKRALPgen}) with $S(T_{\rm ws}) = f_a$ as shown by the black solid line in the lower-right panel, where we take $c_B=0.1$. On the other hand, lepto-ALPgenesis restricts the parameter space to $m_S \gtrsim 30 \TeV$. The axion cannot constitute dark matter via kinetic misalignment in the upper panels due to the warmness constraint in Eq.~(\ref{eq:T_NR}).
002779085 8564_ $$82317811$$s127575$$uhttps://cds.cern.ch/record/2779085/files/fig_ALP-genesis1.png$$y00016 Possible ranges of temperatures are shown for ALP-genesis assuming $c_B=0.1$. Contours of required $f_a$ and $m_S$ are shown by the blue and red lines respectively. White and transparent regions are allowed. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ (left panel) and $6 \times 10^{15} \GeV$ (right panel) become detectable by the experiments specified next to the colored sensitivity curves. The transparent colored shading for each gravitational wave observatory indicates the regions where the peak in the gravitational wave spectrum falls within the experimental sensitivity.
002779085 8564_ $$82317812$$s126765$$uhttps://cds.cern.ch/record/2779085/files/fig_ALP-genesis2.png$$y00017 Possible ranges of temperatures are shown for ALP-genesis assuming $c_B=0.1$. Contours of required $f_a$ and $m_S$ are shown by the blue and red lines respectively. White and transparent regions are allowed. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ (left panel) and $6 \times 10^{15} \GeV$ (right panel) become detectable by the experiments specified next to the colored sensitivity curves. The transparent colored shading for each gravitational wave observatory indicates the regions where the peak in the gravitational wave spectrum falls within the experimental sensitivity.
002779085 8564_ $$82317813$$s77955$$uhttps://cds.cern.ch/record/2779085/files/fig_ALP-genesis-StringGW1.png$$y00028 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82317814$$s74670$$uhttps://cds.cern.ch/record/2779085/files/fig_SGW_earlyKD.png$$y00026 Representative spectra of primordial gravitational waves emitted from local cosmic strings experiencing axion kination (solid) and the standard $\Lambda$CDM cosmology (dashed). Long eras of kination exhibit greater amplitudes in the triangular shaped peak of $\Omega_{\rm GW}h^2$, which is a key signature of axion kination. Of crucial importance is the slowly decaying high frequency tail arising from the sum over high mode numbers which enables detectors like BBO, DECIGO, and CE to detect deviations from the $\Lambda$CDM spectrum even when the kination peak is not located within their frequency domain. Left: Early axion kination cosmology where kination occurs before BBN. The top most contour shows the gravitational wave amplitude when $G\mu$ is fixed to pass through the NANOGrav signal. Right: Late axion kination cosmology where kination occurs in the epoch between CMB and BBN. For each contour, we plot the required $G\mu$ to pass through the NANOGrav signal.
002779085 8564_ $$82317815$$s7405$$uhttps://cds.cern.ch/record/2779085/files/TKR95_CMB.png$$y00003 Posterior distribution for $T_{\rm KR}$ for a late era of kination. We use \emph{Planck} temperature and polarization data (highTTTEEE+lowEE+lowTT) to constrain $T_{\rm{KR}} > 130\, \rm{eV}$ at 95\% (vertical dashed line). See Fig.~\ref{fig:cornerplot} for the complete 2{-}dimensional posterior distributions for $\Lambda\mathrm{CDM} + T_{\mathrm{KR}}$ parameters.
002779085 8564_ $$82317816$$s63214$$uhttps://cds.cern.ch/record/2779085/files/fig_TKR100TeV.png$$y00010 The unshaded regions show the allowed parameter space for axion kination for the fixed values of $T_{\rm KR}$ labeled in each panel. Contours of $T_{\rm MK}$ are shown in these regions with kination. The excluded shaded regions are discussed in the text. To achieve minimal ALPgenesis, the parameter space collapses into $m_S \simeq 5 \keV (0.1/c_B)$ as shown by the black solid line in the upper-right panel, or into $f_a$ given by Eq.~(\ref{eq:TKRALPgen}) with $S(T_{\rm ws}) = f_a$ as shown by the black solid line in the lower-right panel, where we take $c_B=0.1$. On the other hand, lepto-ALPgenesis restricts the parameter space to $m_S \gtrsim 30 \TeV$. The axion cannot constitute dark matter via kinetic misalignment in the upper panels due to the warmness constraint in Eq.~(\ref{eq:T_NR}).
002779085 8564_ $$82317817$$s85112$$uhttps://cds.cern.ch/record/2779085/files/fig_QCDaxionDM2.png$$y00015 Parameter space for the QCD axion dark matter produced by kinetic misalignment, which predicts $T_{\rm KR} \simeq C \times 2 \times 10^{6} \GeV $ as can be seen in Fig.~\ref{fig:axioKD}. The left (right) panel assumes $C = 1~(0.3)$. The regions above the thick magenta and orange lines lead to a primordial gravitation wave signal that can be probed by DECIGO and BBO for the labeled choices of $V_{\rm inf}^{1/4}$, while within the adjacent transparent shadings, the peak of the spectrum can be detected by each observatory. The signal is made possible by the kination era; otherwise, $V_{\rm inf}^{1/4} > 1.2 \times 10^{16} \GeV$ is required for DECIGO.
002779085 8564_ $$82317818$$s88759$$uhttps://cds.cern.ch/record/2779085/files/fig_QCDaxionDM1.png$$y00014 Parameter space for the QCD axion dark matter produced by kinetic misalignment, which predicts $T_{\rm KR} \simeq C \times 2 \times 10^{6} \GeV $ as can be seen in Fig.~\ref{fig:axioKD}. The left (right) panel assumes $C = 1~(0.3)$. The regions above the thick magenta and orange lines lead to a primordial gravitation wave signal that can be probed by DECIGO and BBO for the labeled choices of $V_{\rm inf}^{1/4}$, while within the adjacent transparent shadings, the peak of the spectrum can be detected by each observatory. The signal is made possible by the kination era; otherwise, $V_{\rm inf}^{1/4} > 1.2 \times 10^{16} \GeV$ is required for DECIGO.
002779085 8564_ $$82317819$$s49061$$uhttps://cds.cern.ch/record/2779085/files/fig_Yp.png$$y00001 Primordial helium (left panel) and deuterium (right panel) abundances as a function of $T_{\rm KR}$ and $T_{\rm RM}$, respectively. The gray bands show the experimental constraints.
002779085 8564_ $$82317820$$s50628$$uhttps://cds.cern.ch/record/2779085/files/fig_lateKD.png$$y00029 Left: Required $G\mu$ for $\Omega_{\rm GW}h^2$ to pass through the NANOGrav signal~\cite{NANOGrav:2020bcs,Blasi:2020mfx, Ellis:2020ena}. For long kination eras, which occur when $T_{\rm RM} \gg T_{\rm KR}$, $G\mu$ decreases with respect to the standard $\Lambda$CDM cosmology so that the kination peak does not exceed the NANOGrav signal. Right : The parameter region of axion kination whose imprints on the gravitational wave spectrum from cosmic strings can be detected. For each ($T_{\rm RM},T_{\rm KR})$, we fix $G\mu$ according to the left panel so that spectrum passes through the NANOGrav signal. For the reference $\Lambda$CDM cosmology, we fix $G\mu$ and $\alpha$ to $6 \times 10^{-11}$ and $0.1$, respectively, to also fit NANOGrav. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve of the detector.
002779085 8564_ $$82317821$$s39376$$uhttps://cds.cern.ch/record/2779085/files/fig_EoS.png$$y00000 Scaling evolution of the energy density $\rho$ with scale factor $a$ (left axis) as well as the equation of state $w$ (right axis) as a function of temperature in units of $T_{\rm MK}$, the transition temperature from matter to kination. The colored curves are for the two-field model (blue) and the logarithmic potential (orange), whereas the step function (black) is the piecewise approximation we employ in the remainder of the paper. For the two-field model, we show the blue dotted curves for different ratios of the soft masses of the two fields $\bar{P}$ and $P$, and the blue shading indicates the entire possible range of the model.
002779085 8564_ $$82317822$$s108007$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis6.png$$y00023 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82317823$$s90481$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis4.png$$y00022 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82317824$$s107610$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis5.png$$y00020 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82317825$$s3892269$$uhttps://cds.cern.ch/record/2779085/files/2108.09299.pdf$$yFulltext
002779085 8564_ $$82317826$$s92736$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis3.png$$y00019 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82317827$$s102749$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis1.png$$y00018 Possible ranges of temperatures are shown for lepto-ALP-genesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82317828$$s65050$$uhttps://cds.cern.ch/record/2779085/files/fig_PGW_models.png$$y00011 An illustration of the model dependence in the primordial gravitational wave spectrum. Here we fix $T_{\rm KR} = 10^4 \GeV$, $T_{\rm RM} = 10^8 \GeV$ (and accordingly $T_{\rm MK} \simeq 2 \times 10^5 \GeV$), and the inflationary energy scale $V_{\rm inf}^{1/4} = 10^{16} \GeV$. The black lines are for the case where the rotation energy density $\rho_\theta$ follows a piecewise scaling when $T \lessgtr T_{\rm MK}$ as shown in Fig.~\ref{fig:EoS}. The solid (dashed) black lines are obtained from an analytic (numerical) derivation of the evolution of the metric perturbations. The colored curves are for the two-field model (blue) and the logarithmic potential (orange) with evolution demonstrated in Fig.~\ref{fig:EoS}. For the two-field model, we show the blue dotted curves for different ratios of the soft masses of the two fields $\bar{P}$ and $P$, $m_{\bar P}^2/m_P^2 = 1, 2, \infty$ from top to bottom.
002779085 8564_ $$82317829$$s75183$$uhttps://cds.cern.ch/record/2779085/files/fig_ALP-genesis-StringGW2.png$$y00029 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82317830$$s102303$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis-StringGW2.png$$y00031 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve t
002779085 8564_ $$82317831$$s93491$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALP-genesis-StringGW1.png$$y00030 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82317832$$s72161$$uhttps://cds.cern.ch/record/2779085/files/fig_PGW_1p6e16GeV.png$$y00012 GW spectra from inflation for inflationary energy scale $V_{\rm inf}^{1/4}$ of $1.6 \times 10^{16}$ GeV (left panel) and $6 \times 10^{15}$ GeV (right panel). Each panel contains various choices of $(T_{\rm KR}, T_{\rm RM})$. The left (right) vertex of each triangle approximately indicates the choice of $T_{\rm KR}$ ($T_{\rm RM}$) labeled at the top axis, while $T_{\rm MK}^3 = T_{\rm RM} T_{\rm KR}^2$. The $(T_{\rm KR}, T_{\rm RM})$ choices are $(3 \MeV, 3 \GeV)$ for red, $(10^{-2}, 10^7) \GeV$ for purple, $(10^4, 8 \times 10^7) \GeV$ for blue, and $(10^5, 3 \times 10^9) \GeV$ for brown. Finally, for QCD axion dark matter to be produced by kinetic misalignment with $C = 1$ and $0.3$, $T_{\rm KR}$ is predicted to be $2 \times 10^6$ and $7 \times 10^5$ GeV as shown in the solid and dotted orange curves with the maximal $T_{\rm RM}$ of $7 \times 10^{10}$ and $4 \times 10^{10}$ GeV allowed by the constraints shown in Fig.~\ref{fig:kination_QCD_axion}. These curves assume $g_*(T)$ for the Standard Model and $H$ with individual energy density contributions including a piecewise $\rho_\theta$.
002779085 8564_ $$82317833$$s82339$$uhttps://cds.cern.ch/record/2779085/files/Corner_LCDM_Kination.png$$y00034 Corner plot for the posterior distributions for the $\Lambda$CDM independent parameters and for the axion kination model. We use the highTTTEEE+lowEE+lowTT likelihood combination from \emph{Planck} 2018. Contours contain 68\% and 95\% of the probability.
002779085 8564_ $$82317834$$s70501$$uhttps://cds.cern.ch/record/2779085/files/fig_PGW_6e15GeV.png$$y00013 GW spectra from inflation for inflationary energy scale $V_{\rm inf}^{1/4}$ of $1.6 \times 10^{16}$ GeV (left panel) and $6 \times 10^{15}$ GeV (right panel). Each panel contains various choices of $(T_{\rm KR}, T_{\rm RM})$. The left (right) vertex of each triangle approximately indicates the choice of $T_{\rm KR}$ ($T_{\rm RM}$) labeled at the top axis, while $T_{\rm MK}^3 = T_{\rm RM} T_{\rm KR}^2$. The $(T_{\rm KR}, T_{\rm RM})$ choices are $(3 \MeV, 3 \GeV)$ for red, $(10^{-2}, 10^7) \GeV$ for purple, $(10^4, 8 \times 10^7) \GeV$ for blue, and $(10^5, 3 \times 10^9) \GeV$ for brown. Finally, for QCD axion dark matter to be produced by kinetic misalignment with $C = 1$ and $0.3$, $T_{\rm KR}$ is predicted to be $2 \times 10^6$ and $7 \times 10^5$ GeV as shown in the solid and dotted orange curves with the maximal $T_{\rm RM}$ of $7 \times 10^{10}$ and $4 \times 10^{10}$ GeV allowed by the constraints shown in Fig.~\ref{fig:kination_QCD_axion}. These curves assume $g_*(T)$ for the Standard Model and $H$ with individual energy density contributions including a piecewise $\rho_\theta$.
002779085 8564_ $$82317835$$s8939$$uhttps://cds.cern.ch/record/2779085/files/PS_comparison.png$$y00004 The \emph{linear} matter power spectrum for $\Lambda$CDM and kination cosmology at $z = 0$. For kination cosmology we use $T_{\rm{KR}} = 130 \, \rm{\eV}$ and $T_{\rm{RM}} = 5 \,\rm{\keV}$. Kination leads to an enhanced linear power spectrum above $k \approx \mathcal{O}(1) \, \rm{h/Mpc}$.
002779085 8564_ $$82317836$$s47087$$uhttps://cds.cern.ch/record/2779085/files/fig_D.png$$y00002 Primordial helium (left panel) and deuterium (right panel) abundances as a function of $T_{\rm KR}$ and $T_{\rm RM}$, respectively. The gray bands show the experimental constraints.
002779085 8564_ $$82317837$$s66813$$uhttps://cds.cern.ch/record/2779085/files/fig_TKR100GeV.png$$y00009 The unshaded regions show the allowed parameter space for axion kination for the fixed values of $T_{\rm KR}$ labeled in each panel. Contours of $T_{\rm MK}$ are shown in these regions with kination. The excluded shaded regions are discussed in the text. To achieve minimal ALPgenesis, the parameter space collapses into $m_S \simeq 5 \keV (0.1/c_B)$ as shown by the black solid line in the upper-right panel, or into $f_a$ given by Eq.~(\ref{eq:TKRALPgen}) with $S(T_{\rm ws}) = f_a$ as shown by the black solid line in the lower-right panel, where we take $c_B=0.1$. On the other hand, lepto-ALPgenesis restricts the parameter space to $m_S \gtrsim 30 \TeV$. The axion cannot constitute dark matter via kinetic misalignment in the upper panels due to the warmness constraint in Eq.~(\ref{eq:T_NR}).
002779085 8564_ $$82323511$$s62754$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis-StringGW2.png$$y00033 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82323512$$s57775$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis-StringGW1.png$$y00032 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82323513$$s72535$$uhttps://cds.cern.ch/record/2779085/files/fig_ALPgenesis-StringGW1.png$$y00030 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82323514$$s119446$$uhttps://cds.cern.ch/record/2779085/files/fig_ALPgenesis1.png$$y00016 Possible ranges of temperatures are shown for ALPgenesis assuming $c_B=0.1$. Contours of required $f_a$ and $m_S$ are shown by the blue and red lines respectively. White and transparent regions are allowed. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ (left panel) and $6 \times 10^{15} \GeV$ (right panel) become detectable by the experiments specified next to the colored sensitivity curves. The transparent colored shading for each gravitational wave observatory indicates the regions where the peak in the gravitational wave spectrum falls within the experimental sensitivity.
002779085 8564_ $$82323515$$s62281$$uhttps://cds.cern.ch/record/2779085/files/fig_SGW_bumps.png$$y00025 Left: An illustration of the model dependence in the stochastic string gravitational wave spectrum. The solid black line is the case where the rotation energy density $\rho_{\theta}$ follows a piecewise scaling $T \lessgtr T_{\rm MK}$ as shown in Fig.~\ref{fig:EoS}. The colored curves are for the two-field model (blue) and the logarithmic potential (orange) with evolution demonstrated in Fig.~\ref{fig:EoS}. For the two-field model, we show the blue dotted curves for different ratios of the soft masses of the two fields $\bar{P}$ and $P$, $m_{\bar P}/m_P = 1, 100$. The dashed black curve shows the standard string spectrum in a $\Lambda$CDM cosmology. We fix ($T_{\rm KR}, T_{\rm RM}) = (1 \, {\rm GeV}, 100 \, {\rm GeV})$. Right: An illustration of the difference between the $m = 1$ amplitude (purple) and the total amplitude summed over $10^4$ harmonics (red). The sum over high modes partially flattens the right side of the kination induced peak, shifting the spectral dependence from $f^{-1}$ to $f^{-1/3}$. We fix ($T_{\rm KR}, T_{\rm RM}) = (1 \GeV, 10 \TeV)$. In both panels, the second, smaller triangle at high frequencies is an additional fingerprint of axion kination and arises from loops that form in the early radiation dominated era and decay in the subsequent matter or kination dominated eras (see Table \ref{tab:frequencyDependence}). Both panels assume $G\mu = 5 \times 10^{-15}$, and $\alpha = 0.1$. The drop in the spectrum above $f \sim 10^{12}$ Hz arises from only considering loops that form after the string network reaches scaling, $t_k > t_{\rm scl}$. We take scaling to be reached shortly after string formation, $t_k \sim 1/H(T = \sqrt{\mu})$. However, string friction with the thermal bath can delay scaling and shift this high frequency cutoff to lower frequencies \cite{Alford:1988sj,Vilenkin:1991zk,vilenkin2000cosmic,Gouttenoire:2019kij}. We do not include this model dependent effect in this work.
002779085 8564_ $$82323516$$s67620$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis2.png$$y00021 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323517$$s58434$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis3.png$$y00019 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323518$$s69344$$uhttps://cds.cern.ch/record/2779085/files/fig_ALPgenesis-StringGW2.png$$y00031 Detector reach of the kination cosmic string gravitational wave spectrum for a range of $T_{\rm KR}$ and $T_{\rm MK}$ consistent with minimal ALPgenesis (top) and lepto-ALPgenesis (bottom). The top-right panel zooms in on the bottom-left part of the top-left panel. $G\mu$ and $\alpha$ are fixed at $6 \times 10^{-11}$ and $0.1$, respectively, to fit the NANOGrav data~\cite{NANOGrav:2020bcs}. For a given $(T_{\rm KR}, T_{\rm MK})$, a detection is registered when the difference in amplitudes, $\Omega_{\rm GW} - \Omega_{\rm GW,0}$ is greater than $10\%$ (solid) or 100\% (dashed) of the standard cosmological amplitude, $\Omega_{\rm GW,0}$, within the sensitivity curve the detector. In the transparent shared regions, the peak of the spectrum originated from axion kination can be detected.
002779085 8564_ $$82323519$$s66807$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis1.png$$y00018 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323520$$s70281$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis6.png$$y00023 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323521$$s57467$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis4.png$$y00022 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323522$$s69152$$uhttps://cds.cern.ch/record/2779085/files/fig_lepto-ALPgenesis5.png$$y00020 Possible ranges of temperatures are shown for lepto-ALPgenesis. The left two columns are for the case with entropy production from saxion domination ($D = 1$), while the right column assumes radiation domination ($D = \mathcal{O}(20)$) with degenerated neutrinos. These different cases are explained in Sec.~\ref{subsec:baryogenesis} and Ref.~\cite{Co:2020jtv}. The dark matter abundance is explained by an appropriate ALP mass determined by $f_a$ and $T_{\rm KR}$ using Fig.~\ref{fig:axioKD}. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ ($6 \times 10^{15} \GeV$) in the upper (lower) panels become detectable by the experiments labeled next to the colored sensitivity curves. The transparent colored shadings indicate that the peak of the gravitational wave spectrum due to kination lies inside the corresponding experimental reach.
002779085 8564_ $$82323523$$s119105$$uhttps://cds.cern.ch/record/2779085/files/fig_ALPgenesis2.png$$y00017 Possible ranges of temperatures are shown for ALPgenesis assuming $c_B=0.1$. Contours of required $f_a$ and $m_S$ are shown by the blue and red lines respectively. White and transparent regions are allowed. Thanks to a kination era, the primordial gravitational waves for $V_{\rm inf}^{1/4} = 10^{16} \GeV$ (left panel) and $6 \times 10^{15} \GeV$ (right panel) become detectable by the experiments specified next to the colored sensitivity curves. The transparent colored shading for each gravitational wave observatory indicates the regions where the peak in the gravitational wave spectrum falls within the experimental sensitivity.
002779085 8564_ $$82323524$$s50506$$uhttps://cds.cern.ch/record/2779085/files/fig_SGW_models.png$$y00024 Left: An illustration of the model dependence in the stochastic string gravitational wave spectrum. The solid black line is the case where the rotation energy density $\rho_{\theta}$ follows a piecewise scaling $T \lessgtr T_{\rm MK}$ as shown in Fig.~\ref{fig:EoS}. The colored curves are for the two-field model (blue) and the logarithmic potential (orange) with evolution demonstrated in Fig.~\ref{fig:EoS}. For the two-field model, we show the blue dotted curves for different ratios of the soft masses of the two fields $\bar{P}$ and $P$, $m_{\bar P}/m_P = 1, 100$. The dashed black curve shows the standard string spectrum in a $\Lambda$CDM cosmology. We fix ($T_{\rm KR}, T_{\rm RM}) = (1 \, {\rm GeV}, 100 \, {\rm GeV})$. Right: An illustration of the difference between the $m = 1$ amplitude (purple) and the total amplitude summed over $10^4$ harmonics (red). The sum over high modes partially flattens the right side of the kination induced peak, shifting the spectral dependence from $f^{-1}$ to $f^{-1/3}$. We fix ($T_{\rm KR}, T_{\rm RM}) = (1 \GeV, 10 \TeV)$. In both panels, the second, smaller triangle at high frequencies is an additional fingerprint of axion kination and arises from loops that form in the early radiation dominated era and decay in the subsequent matter or kination dominated eras (see Table \ref{tab:frequencyDependence}). Both panels assume $G\mu = 5 \times 10^{-15}$, and $\alpha = 0.1$. The drop in the spectrum above $f \sim 10^{12}$ Hz arises from only considering loops that form after the string network reaches scaling, $t_k > t_{\rm scl}$. We take scaling to be reached shortly after string formation, $t_k \sim 1/H(T = \sqrt{\mu})$. However, string friction with the thermal bath can delay scaling and shift this high frequency cutoff to lower frequencies \cite{Alford:1988sj,Vilenkin:1991zk,vilenkin2000cosmic,Gouttenoire:2019kij}. We do not include this model dependent effect in this work.
002779085 8564_ $$82423369$$s3364540$$uhttps://cds.cern.ch/record/2779085/files/document.pdf$$yFulltext
002779085 8564_ $$82563651$$s81846$$uhttps://cds.cern.ch/record/2779085/files/fig_Corner_LCDM_Kination.png$$y00034 Corner plot for the posterior distributions for the $\Lambda$CDM independent parameters and for the axion kination model. We use the highTTTEEE+lowEE+lowTT likelihood combination from \textit{Planck} 2018. Contours contain 68\% and 95\% of the probability.
002779085 8564_ $$82563652$$s5114$$uhttps://cds.cern.ch/record/2779085/files/fig_TKR95_CMB.png$$y00003 Posterior distribution for $T_{\rm KR}$ for a late era of kination. We use \textit{Planck} temperature and polarization data (highTTTEEE+lowEE+lowTT) to constrain $T_{\rm{KR}} > 50\, \rm{eV}$ at 95\% (vertical dashed line). See Fig.~\ref{fig:cornerplot} for the complete 2{-}dimensional posterior distributions for $\Lambda\mathrm{CDM} + T_{\mathrm{KR}}$ parameters.
002779085 8564_ $$82563653$$s7395$$uhttps://cds.cern.ch/record/2779085/files/fig_PS_comparison.png$$y00004 The \emph{linear} matter power spectrum for $\Lambda$CDM and kination cosmology at $z = 0$. For kination cosmology we use $T_{\rm{KR}} = 50 \, \rm{\eV}$ and $T_{\rm{RM}} = 5 \,\rm{\keV}$. Kination leads to an enhanced linear power spectrum above $k \approx \mathcal{O}(1) \, \rm{h/Mpc}$.
002779085 8564_ $$82563654$$s44219$$uhttps://cds.cern.ch/record/2779085/files/fig_Corner_LCDM_Kination_parameters.png$$y00035 Corner plot for the posterior distributions for the calculated values $\Lambda$CDM parameters and axion kination cosmology. Contours contain 68\% and 95\% of the probability.
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