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Register a new userReheating through the Higgs amplified by spinodal instabilities and gravitational creation of gravitons
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It is shown that a positive non-minimal coupling of the Higgs field to gravity can solve the two problems in inflation models in which postinflationary universe is dominated by an energy with stiff equation of state such as a kination, namely, overproduction of gravitons in gravitational reheating scenario, and overproduction of curvature perturbation from Higgs condensation. Furthermore, we argue that the non-minimal coupling parameter can be constrained more stringently with the progress in observations of large-scale structure and cosmic microwave background.
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It is well known that the inflationary scenario often displays different sets of degeneracies in its predictions for CMB observables. These degeneracies usually arise either because multiple inflationary models predict similar values for the scalar spectral index $n_{_S}$ and the tensor-to-scalar ratio $r$, or because within the same model, the values of $lbrace n_{_S}, r rbrace$ are insensitive to some of the model parameters, making it difficult for CMB observations alone to constitute a unique probe of inflationary cosmology. We demonstrate that by taking into account constraints on the post-inflationary reheating parameters such as the duration of reheating $N_{_{rm re}}$, its temperature $T_{_{rm re}}$ and especially its equation of state (EOS), $w_{_{rm re}}$, it is possible to break this degeneracy in certain classes of inflationary models where identical values of $lbrace n_{_S}, r rbrace$ can correspond to different reheating $w_{_{rm re}}$. In particular, we show how reheating constraints can break inflationary degeneracies in the T-model and the E-model $alpha$-attractors. Non-canonical inflation is also studied. The relic gravitational wave (GW) spectrum provides us with another tool to break inflationary degeneracies. This is because the GW spectrum is sensitive to the post-inflationary EOS of the universe. Indeed a stiff EOS during reheating $(w_{_{rm re}} > 1/3)$ gives rise to a small scale blue tilt in the spectral index $n_{_{rm GW}} = frac{dlog{Omega_{_{rm GW}}}}{dlog{k}} > 0$, while a soft EOS $(w_{_{rm re}} < 1/3)$ results in a red tilt. Relic GWs therefore provide us with valuable information about the post-inflationary epoch, and their spectrum can be used to cure inflationary degeneracies in $lbrace n_{_S}, rrbrace$.
We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary e-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21cm cosmology.
The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at present, at the end of inflation, and at horizon-exit, to the 2-nd adiabatic order for the spectrum, and the 4-th order for energy density and pressure. In the first scheme a cutoff is needed to remove graviton divergences. We find that all three schemes yield the spectra of a similar profile, and the primordial spectrum defined far outside horizon during inflation is practically unaffected. We also regularize the gauge-invariant perturbed inflaton and the scalar curvature perturbation by the last two schemes, and find that the scalar spectra, the tensor-to-scalar ratio, and the consistency relation remain unchanged.
We study the evolution of Gravitational Waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass $m_g$ that depends either on the inflaton field $phi$ or on its time derivative $dot{phi}$, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinskys $R^2$ inflation model with a $phi$-dependent $m_g$ and the second is a low-energy-scale inflation model with a $dot{phi}$-dependent $m_g$. We compute the energy density spectrum $Omega_{rm GW}(k)$ today of the GW background. In the Starobinskys model, we show that the GWs can be amplified up to the detectable ranges of both CMB and DECIGO, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential $V(phi)=M^2 phi^2/2$ around $phi approx M_{rm pl}$ (where $M_{rm pl}$ is the reduced Planck mass), we find that the peak position of $Omega_{rm GW}(k)$ induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.
It is well known that the Klein Gordon (KG) equation $Box Phi + m^2Phi=0$ has tachyonic unstable modes on large scales ($k^2<vert m vert^2$) for $m^2<m_{cr}^2=0$ in a flat Minkowski spacetime with maximum growth rate $Omega_{F}(m)= vert m vert$ achieved at $k=0$. We investigate these instabilities in a Reissner-Nordstrom-deSitter (RN-dS) background spacetime with mass $M$, charge $Q$, cosmological constant $Lambda>0$ and multiple horizons. By solving the KG equation in the range between the event and cosmological horizons, using tortoise coordinates $r_*$, we identify the bound states of the emerging Schrodinger-like Regge-Wheeler equation corresponding to instabilities. We find that the critical value $m_{cr}$ such that for $m^2<m_{cr}^2$ bound states and instabilities appear, remains equal to the flat space value $m_{cr}=0$ for all values of background metric parameters despite the locally negative nature of the Regge-Wheeler potential for $m=0$. However, the growth rate $Omega$ of tachyonic instabilities for $m^2<0$ gets significantly reduced compared to the flat case for all parameter values of the background metric ($Omega(Q/M,M^2 Lambda, mM)< vert m vert$). This increased lifetime of tachyonic instabilities is maximal in the case of a near extreme Schwarzschild-deSitter (SdS) black hole where $Q=0$ and the cosmological horizon is nearly equal to the event horizon ($xi equiv 9M^2 Lambda simeq 1$). The physical reason for this delay of instability growth appears to be the existence of a cosmological horizon that tends to narrow the negative range of the Regge-Wheeler potential in tortoise coordinates.
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