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Register a new userEnhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era
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We study gravitational waves induced from the primordial scalar perturbations at second order around the reheating of the Universe. We consider reheating scenarios in which a transition from an early matter dominated era to the radiation dominated era completes within a timescale much shorter than the Hubble time at that time. We find that an enhanced production of induced gravitational waves occurs just after the reheating transition because of fast oscillations of scalar modes well inside the Hubble horizon. This enhancement mechanism just after an early matter-dominated era is much more efficient than a previously known enhancement mechanism during an early matter era, and we show that the induced gravitational waves could be detectable by future observations if the reheating temperature $T_{text{R}}$ is in the range $T_text{R} lesssim 7times 10^{-2}$GeV or $20 , text{GeV} lesssim T_text{R} lesssim 2 times 10^7 , text{GeV}$. This is the case even if the scalar perturbations on small scales are not enhanced relative to those on large scales, probed by the observations of the cosmic microwave background.
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We revisit the effects of an early matter-dominated era on gravitational waves induced by scalar perturbations. We carefully take into account the evolution of the gravitational potential, the source of these induced gravitational waves, during a gradual transition from an early matter-dominated era to the radiation-dominated era, where the transition timescale is comparable to the Hubble time at that time. Realizations of such a gradual transition include the standard perturbative reheating with a constant decay rate. Contrary to previous works, we find that the presence of an early matter-dominated era does not necessarily enhance the induced gravitational waves due to the decay of the gravitational potential around the transition from an early matter-dominated era to the radiation-dominated era.
We investigate the generation of gravitational waves due to the gravitational instability of primordial density perturbations in an early matter-dominated era which could be detectable by experiments such as LIGO and LISA. We use relativistic perturbation theory to give analytic estimates of the tensor perturbations generated at second order by linear density perturbations. We find that large enhancement factors with respect to the naive second-order estimate are possible due to the growth of density perturbations on sub-Hubble scales. However very large enhancement factors coincide with a breakdown of linear theory for density perturbations on small scales. To produce a primordial gravitational wave background that would be detectable with LIGO or LISA from density perturbations in the linear regime requires primordial comoving curvature perturbations on small scales of order 0.02 for Advanced LIGO or 0.005 for LISA, otherwise numerical calculations of the non-linear evolution on sub-Hubble scales are required.
We calculate the gravitational wave background produced from density perturbations in an early matter domination era where primordial black holes form. The formation of black holes requires perturbations out of the linear regime. Space with such perturbations reach a maximum expansion before it collapses asymmetrically forming a Zeldovich pancake which depending on the parameters can either lead to a black hole or a virialized halo. In both cases and due to the asymmetry of the collapsing matter, a quadrupole moment generates gravitational waves which leave an imprint in the form of a stochastic background that can be detectable by near future gravitational interferometers.
Assuming that inflation is succeeded by a phase of matter domination, which corresponds to a low temperature of reheating $T_r<10^9rm{GeV}$, we evaluate the spectra of gravitational waves induced in the post-inflationary universe. We work with models of hilltop-inflation with an enhanced primordial scalar spectrum on small scales, which can potentially lead to the formation of primordial black holes. We find that a lower reheat temperature leads to the production of gravitational waves with energy densities within the ranges of both space and earth based gravitational wave detectors.
We put the upper bound on the gravitational waves (GWs) induced by the scalar-field fluctuations during the inflation. In particular, we focus on the case where the scalar fluctuations get amplified within some subhorizon scales by some mechanism during the inflation. Since the energy conservation law leads to the upper bound on the energy density of the scalar fluctuations, the amplitudes of the scalar fluctuations are constrained and therefore the induced GWs are also. Taking into account this, we derive the upper bound on the induced GWs. As a result, we find that the GW power spectrum must be $mathcal P_h lesssim mathcal O(epsilon^2 (k/k_*)^2)$, where $epsilon$ is the slow-roll parameter and $k_*$ is the peak scale of the scalar-field fluctuations.
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