Dissipative Axial Inflation

Notari, Alessio; Tywoniuk, Konrad

doi:10.1088/1475-7516/2016/12/038

Article
Report number	arXiv:1608.06223 ; CERN-TH-2016-189
Title	Dissipative Axial Inflation
Related title	Dissipative Axial Inflation
Author(s)	Notari, Alessio (Barcelona U., Dept. Fund. Phys. ; ICC, Barcelona U.) ; Tywoniuk, Konrad (CERN)
Publication	2016-12-22
Imprint	22 Aug 2016
Number of pages	23
Note	Comments: 22 pages, 27 figures 22 pages, 27 figures
In:	JCAP 12, 12 (2016) pp.038
DOI	10.1088/1475-7516/2016/12/038 10.1088/1475-7516/2016/12/038
Subject category	Particle Physics - Theory
Abstract	We analyze in detail the background cosmological evolution of a scalar field coupled to a massless abelian gauge field through an axial term $\frac{\phi}{f_\gamma} F \tilde{F}$, such as in the case of an axion. Gauge fields in this case are known to experience tachyonic growth and therefore can backreact on the background as an effective dissipation into radiation energy density $\rho_R$, which which can lead to inflation without the need of a flat potential. We analyze the system, for momenta $k$ smaller than the cutoff $f_\gamma$, including numerically the backreaction. We consider the evolution from a given static initial condition and explicitly show that, if $f_\gamma$ is smaller than the field excursion $\phi_0$ by about a factor of at least ${\cal O} (20)$, there is a friction effect which turns on before that the field can fall down and which can then lead to a very long stage of inflation with a generic potential. In addition we find superimposed oscillations, which would get imprinted on any kind of perturbations, scalars and tensors. Such oscillations have a period of 4-5 efolds and an amplitude which is typically less than a few percent and decreases linearly with $f_\gamma$. We also stress that the comoving curvature perturbation on uniform density should be sensitive to slow-roll parameters related to $\rho_R$ rather than $\dot{\phi}^2/2$, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply define and compute suitable slow roll parameters. Finally we stress that this scenario may be realized in the axion case, if the coupling $1/f_\gamma$ to U(1) (photons) is much larger than the coupling $1/f_G$ to non-abelian gauge fields (gluons), since the latter sets the range of the potential and therefore the maximal allowed $\phi_0\sim f_G$.
Copyright/License	arXiv nonexclusive-distrib. 1.0

$We show the time evolution, in a quadratic potential and in flat spacetime, of the growing gauge field $A_{-}$, for increasing values of $k$, from $k_{\rm min}=f_\gamma/300$ to $k_{\rm max}=f_\gamma$, equally spaced in logarithmic scale. In dashed lines we show the same modes, in absence of backreaction.$ $We show in the left panel the backreaction spectrum $P_{\cal B}(k)$, defined in eq.~(\ref{spectrum}), at three different times during the evolution, using a quadratic potential and in flat spacetime. In the right panel we show the spectrum of electromagnetic energy density $P_{\rho_R}(k)$, and also the vacuum energy density, which should be subtracted by renormalization. For both cases the flat region of the spectrum becomes wider as time goes on, since more infrared modes have enough time to get excited. The thin pink line represents the growth of modes in absence of backreaction, at a given time.$ $We show in the left panel the backreaction spectrum $P_{\cal B}(k)$, defined in eq.~(\ref{spectrum}), at three different times during the evolution, using a quadratic potential and in flat spacetime. In the right panel we show the spectrum of electromagnetic energy density $P_{\rho_R}(k)$, and also the vacuum energy density, which should be subtracted by renormalization. For both cases the flat region of the spectrum becomes wider as time goes on, since more infrared modes have enough time to get excited. The thin pink line represents the growth of modes in absence of backreaction, at a given time.$ Show more plots

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