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Register a new userHigh-frequency Graviton from Inflaton Oscillation
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We point out that there is a high-frequency tail of the stochastic inflationary gravitational wave background that scales as $f^{-1/2}$ with frequency $f$. This contribution comes from the graviton vacuum fluctuation amplified by the inflaton coherent oscillation during the reheating stage. It contains information on inflaton properties such as the inflaton mass as well as the thermal history of the early Universe.
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We study the conditions under which simple relations between the inflaton couplings and CMB observables can be established. The crucial criterion is to avoid feedback effects during reheating, which tend to introduce a complicated dependence of the CMB observables on a large number of microphysical parameters that prohibits the derivation of meaningful constraints on any individual one of them. We find that the inflaton coupling can be measured with cosmological data when the effective potential during reheating can be approximated by a parabola, and when the coupling constants are smaller than an upper bound that it determined by the ratios between the inflaton mass and the Planck mass or the scale of inflation. The power at which these ratios appear is determined by the power at which the inflaton appears in a given interaction term, and the value of the upper bound is largely independent of the type of produced particle. Our results show that next generation CMB observatories may be able to constrain the inflaton couplings for various types of interactions, providing an important clue to understand how a given model of inflation may be embedded into a more fundamental microphysical theory of nature.
We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow roll approximation that allows large amplitude, rapidly changing deviations from scale-free conditions. Employing a principal component decomposition of the source function G~3(V/V)^2 - 2V/V and keeping only those measured to better than 10% results in 5 nearly independent Gaussian constraints that maybe used to test any single-field inflationary model where such deviations are expected. The first component implies < 3% variations at the 100 Mpc scale. One component shows a 95% CL preference for deviations around the 300 Mpc scale at the ~10% level but the global significance is reduced considering the 5 components examined. This deviation also requires a change in the cold dark matter density which in a flat LCDM model is disfavored by current supernova and Hubble constant data and can be tested with future polarization or high multipole temperature data. Its impact resembles a local running of the tilt from multipoles 30-800 but is only marginally consistent with a constant running beyond this range. For this analysis, we have implemented a ~40x faster WMAP7 likelihood method which we have made publicly available.
Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1sim -2/N$, where $N$ is the number of e-foldings. Quadratic chaotic model, Starobinsky model and Higgs inflation or $alpha$-attractors connecting them are typical examples predicting such a relation. We consider the problem in the opposite: given $n_s$ as a function of $N$, what is the inflaton potential $V(phi)$. We find that for $n_s-1=-2/N$, $V(phi)$ is either $tanh^2(gammaphi/2)$ (T-model) or $phi^2$ (chaotic inflation) to the leading order in the slow-roll approximation. $gamma$ is the ratio of $1/V$ at $Nrightarrow infty$ to the slope of $1/V$ at a finite $N$ and is related to $alpha$ in the $alpha$-attractors by $gamma^2=2/3alpha$. The tensor-to-scalar ratio $r$ is $r=8/N(gamma^2 N +1) $. The implications for the reheating temperature are also discussed. We also derive formulas for $n_s-1=-p/N$. We find that if the potential is bounded from above, only $p>1$ is allowed. Although $r$ depends on a parameter, the running of the spectral index is independent of it, which can be used as a consistency check of the assumed relation of $n_s(N)$.
We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(phi)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(phi)$ has the unique property that it is the solution to the brachistochrone problem for inflation.
In this work, we present the first experimental upper limits on the presence of stochastic ultra-high-frequency gravitational waves. We exclude gravitational waves in the frequency bands from $(2.7 - 14)times10^{14}~$Hz and $(5 - 12)times10^{18}~$Hz down to a characteristic amplitude of $h_c^{rm min}approx6times 10^{-26}$ and $h_c^{rm min}approx 5times 10^{-28}$ at $95~$% confidence level, respectively. To obtain these results, we used data from existing facilities that have been constructed and operated with the aim of detecting WISPs (Weakly Interacting Slim Particles), pointing out that these facilities are also sensitive to gravitational waves by graviton to photon conversion in the presence of a magnetic field. The principle applies to all experiments of this kind, with prospects of constraining (or detecting), for example, gravitational waves from light primordial black hole evaporation in the early universe.
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