We investigate the generation of gravitational waves in power-law inflationary models. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients. We show that, by looking at the interval of frequencies between 10^(-5) and 10^5 Hz and also at the GHz range, important information can be obtained, both about the inflationary period itself and about the thermalization regime between the end of inflation and the beginning of the radiation-dominated era. We thus deem the development of gravitational wave detectors, covering the MHz/GHz range of frequencies, to be an important task for the future.
Improved general slow-roll formulae giving the primordial gravitational wave spectrum are derived in the present work. Also the first and second order general slow-roll inverse formulae giving the Hubble parameter $H$ in terms of the gravitational wave spectrum are derived. Moreover, the general slow-roll consistency condition relating the scalar and tensor spectra is obtained.
Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral index of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. He…
We give the initial spectrum of quantized gravitational waves in the context of the one-bubble open inflationary universe scenario. In determining the quantum state after the bubble nucleation we adopt the prescription to require the analyticity of positive frequency functions in half of the Euclidean extension of the background O(3,1)-symmetric spacetime. We find the spectrum is well behaved at the infrared limit and there appears no supercurvature mode. In the thin wall approximation, the explicit form of the spectrum of gravitational wave perturbations is calculated.
We study the implications of recent indications for a red spectrum of primordial density perturbations for the detection of inflationary gravitational waves (IGWs) with forthcoming cosmic microwave background experiments. We find that if inflation occurs with a single field with an inflaton potential minimized at V=0, then Planck will be able to detect IGWs at better than 2$σ$ confidence level, unless the inflaton potential is a power law with a very weak power. The proposed satellite missions of the Cosmic Vision and Inflation Probe programs will be able to detect IGWs from all the models we …
In addition to density perturbations, inflationary models of the early universe generally predict a stochastic background of gravitational waves or tensor fluctuations. By making use of the inflationary flow approach for single field models and fitting the models with Monte-Carlo techniques to cosmic microwave background (CMB) data from the {\it Wilkinson Microwave Anisotropy Probe} (WMAP), we discuss the expected properties of the gravitational wave background from inflation at scales corresponding to direct detection experiments with laser interferometers in space. We complement the Monte-Ca…
Physical scenarios, leading to highly energetic stochastic gravitational waves backgrounds (for frequencies ranging from the $μ$Hz up to the GHz) are examined. In some cases the typical amplitude of the logarithmic energy spectrum can be even eight orders of magnitude larger than the ordinary inflationary prediction. Scaling violations in the frequency dependence of the energy density of the produced gravitons are discussed.
The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and unifor…
We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wron…
As the strong evidence for inflation, the relic gravitational waves (RGW) have been extensively studied. Although, it has not been detected, yet some constraints have been achieved by the observations. Future experiments for the RGW detection are mainly two kinds: the CMB experiments and the laser interferometers. In this paper, we study these current constraints and the detective abilities of future experiments. We calculate the strength of RGW $Ω_g(k)$ in two methods: the analytic method and the numerical method by solving the inflationary flow equations. By the first method we obtain a boun…
We investigate the possibility for a direct detection by future space interferometers of the stochastic gravitational wave (GW) background generated during the inflationary stage in a class of viable $Λ$CDM BSI models. At frequencies around $10^{-3}$Hz, maximal values $Ω_{gw}(ν)\sim 3\times 10^{-15}$ are found, an improvement of about one order of magnitude compared to single-field, slow-roll inflationary models. This is presumably not sufficient in order to be probed in the near future.
Inflation generically predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO) or Japan's Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO), both currently under study. Here we investigate the detectability of the inflationary gravitational-wave background at BBO/DECIGO frequencies. To do so, we survey a range of slow-roll inflationary models consistent with constraints from …
Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. We explicitly calculate this spectrum for bot…
We consider gravitational wave production due to parametric resonance at the end of inflation, or ``preheating''. This leads to large inhomogeneities which source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale. We analyze an explicit model where the inflationary energy scale is ~10^9 GeV, yielding a signal close to the sensitivity of Advanced LIGO and BBO. This signal highlights the possibility of a new observa…
Inflation predicts specific relations between the amplitudes and spectral indices of the primordial spectrum of density (scalar metric) perturbations and gravitational waves (tensor metric perturbations). Detection of a stochastic gravitational-wave background is essential for identifying this unmistakable signature. Polarization of the cosmic microwave background can isolate these tensor modes in a model-independent way and thereby circumvent the cosmic-variance limit to detecting a small tensor signal with only a temperature map. Here we assess the detectability of a gravity-wave background …
We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form $a(η)=c_1η^2+c_2η+c_3$, where $c_i$ are constants. During the mixed phase the universe smoothly transforms from being radiation to dust dominated. We find analytic expressions for the graviton mode func…
Primordial gravitational waves are created during the de Sitter phase of an exponentially-expanding (inflationary) universe, due to quantum zero-point vacuum fluctuations. These waves produce fluctuations in the temperature of the Cosmic Background Radiation (CBR). We calculate the multipole moments of the correlation function for these temperature fluctuations in a spatially-closed Friedman-Robertson-Walker (FRW) cosmological model. The results are compared to the corresponding multipoles in the spatially-flat case. The differences are small unless the density parameter today, $Ω_0$, is great…
We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. These temperature fluctuations are described by an angular correlation function $C(γ)$. A new (more concise and general) derivation of $C(γ)$ is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles $γ$ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode …
We review current observational constraints on the polarization of the Cosmic Microwave Background (CMB), with a particular emphasis on detecting the signature of primordial gravitational waves. We present an analytic solution to the Polanarev approximation for CMB polarization produced by primordial gravitational waves. This simplifies the calculation of the curl, or B-mode power spectrum associated with gravitational waves during the epoch of cosmological inflation. We compare our analytic method to existing numerical methods and also make predictions for the sensitivity of upcoming CMB pola…
The gravitational waves (GW) background generated in a double inflationary model, with two scalar fields mutually interacting through gravity only, and its relative contribution $T/S$ to large-angle temperature fluctuations of the relic microwave background are investigated in detail. The relation between $T/S$ and the slope of the GW spectrum $n_T$ is shown to be a discriminative test between a slow-roll inflation driven by one scalar field and more complicated models. It is found that the GW amplitude is not exactly zero in minima of spectral oscillations, this property being an observationa…
We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the super-inflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts CMB observations. To circum…
A generic outcome of theories with scalar-tensor coupling is the existence of inflationary attractors, either power-law or de Sitter. The fluctuations arising during this phase are Gaussian and their spectrum depends on the wavenumber $k$ according to the power-law $k^{1/(1-p)}$, where $p$ is the inflationary power-law exponent. We investigate to which extent these properties depend on the coupling function and on the potential. We find the class of models in which viable attractors exist. Within this class, we find that the cosmic expansion and the scaling of the fluctuation spectrum are inde…
We study the evolution of gravitational waves(GWs) after inflation in a brane-world cosmology embedded in five-dimensional anti-de Sitter spacetime. Contrary to the standard four-dimensional results, the GWs at the high-energy regime in brane-world model suffer from the effects of the non-standard cosmological expansion and the excitation of the Kaluza-Klein modes(KK-modes), which can affect the amplitude of stochastic gravitational wave background significantly. To investigate these two high-energy effects quantitatively, we numerically solve the wave equation of the GWs in the radiation domi…
We demonstrate the parametric amplification of the stochastic gravitational wave background during inflationary reheating and during axion/moduli oscillations. This amplification enhances the detectability of the string/inflationary gravity wave signal, leaving a finger-print on the spectrum which might be found with future gravitational wave detectors.
We point out that the existence of post-inflationary phases stiffer than radiation leads to the production of stochastic gravitational waves (GW) backgrounds whose logarithmic energy spectra (in critical units) are typically "blue" at high frequencies. The maximal spectral slope (for present frequencies larger than $10^{-16}$ Hz) is of order one and it is related to the maximal sound velocity of the stiff plasma governing the evolution of the geometry. The duration of the stiff phase is crucially determined by the backreaction of the GW leaving the horizon during the de Sitter phase and re-ent…
In this paper we study the behaviour of gravitational wave background (GWB) generated during inflation in the environment of the noncommutative field approach. From this approach we derive out one additive term, and then we find that the dispersion relation of the gravitational wave would be modified and the primordial gravitational wave would obtain an effective mass. Therefore it breaks lorentz symmetry in local. Moreover, this additive term would a little raise up the energy spectrum of GWB in low frequency and then greatly suppress the spectrum at even lower energy scale of which the wave …
According to the Brans--Dicke theory, the value of the gravitational constant G which we measure at present is determined by the value of the Brans--Dicke scalar field ϕat the end of inflation. However, due to quantum fluctuations of the scalar fields produced during inflation, the gravitational constant G(ϕ) may take different values in different exponentially large parts of the Universe. We investigate the probability distribution P_p to find a domain of a given volume with a given value of the gravitational constant G at a given time. The investigation is performed for a wide class of effec…
We investigate the cosmological evolution of gravitational waves in Friedman-Robertson-Walker brane world models embedded in a five dimensional anti de-Sitter spacetime. To predict the spectrum of stochastic gravitational background at present generated in the inflationary phase, we numerically calculate the evolution of gravitational waves according to the method developed in our previous paper [K. Ichiki and K. Nakamura, arXiv:hep-th/0310282]. The resulting logarithmic energy spectrum is significantly altered from that of the standard four dimensional inflationary models in the frequency ran…
In non-oscillatory (NO) inflationary models, the reheating mechanism was usually based on gravitational particle production or the mechanism of instant preheating. In this paper we introduce the curvaton mechanism into NO models to reheat the universe and generate the curvature perturbation. Specifically we consider the Peebles-Vilenkin quintessential inflation model, where the reheating temperature can be extended from 1MeV to $10^{13}$GeV.
The Cosmic Microwave Background Radiation (CMBR) holds information about almost all the fundamental cosmological parameters, and by performing a likelihood analysis of high precision CMBR fluctuation data, these parameters can be inferred. However, this analysis relies on assumptions about the initial power spectrum, which is usually taken to be a featureless power-law, P(k) ~ k^{n_s-1}. Many inflationary models predict power spectra with non-power law features. We discuss the possibility for detecting such features by describing the power spectrum as bins in k-space. This method for power spe…
We supply fitting formulae enabling the normalization of slow-roll inflation models to the four-year COBE data. We fully include the effect of the gravitational wave modes, including the predicted relation of the amplitude of these modes to that of the density perturbations. We provide the normalization of the matter power spectrum, which can be directly used for large-scale structure studies. The normalization for tilted spectra is a special case. We also provide fitting functions for the inflationary energy scale of COBE-normalized models and discuss the validity of approximating the spectra…
We discuss the cosmological evolution of the inflationary gravitational wave background (IGWB) in the Randall-Sundrum single-brane model. In the braneworld cosmology, in which three-dimensional space-like hypersurface that we live in is embedded in five-dimensional anti de Sitter (AdS_5) space-time, the evolution of gravitational wave (GW) modes is affected by the non-standard expansion of the universe and the excitation of the Kaluza-Klein modes (KK-modes), which are significant in the high-energy regime of the universe. We numerically evaluate these two effects by solving the evolution equat…
Near comoving wavenumber k, the gravitational-wave background (GWB) from inflation carries information about the physical conditions near two moments in cosmic history: the moment when k ``left the horizon'' during inflation, and the moment when it ``re-entered the horizon'' after inflation. We investigate the extent to which this information can be extracted if the GWB is measured by a combination of cosmic-microwave-background (CMB) polarization experiments on large scales and space-based laser-interferometer experiments on small scales. To disentangle this information, we derive a new gravi…
The generation of large-scale magnetic fields is studied in inflationary cosmology. We consider the violation of the conformal invariance of the Maxwell field by dilatonic as well as non-minimal gravitational couplings. We derive a general formula for the spectrum of large-scale magnetic fields for a general form of the coupling term and the formula for the spectral index. The result tells us clearly the (necessary) condition for the generation of magnetic fields with sufficiently large amplitude.
The recent three-year WMAP data selects large-field models with certain power-law potentials and small-field models for all power-law potentials as consistent inflation models. We study the large-field and small-field inflation model with a quadratic and a quartic potential within the framework of quantum field theory in an expanding Friedmann-Robertson-Walker universe. We find that quantum fluctuations in the small-field model lead to a significant contribution to the effective potential and may have non-negligible effects on the slow-roll parameters predicted by classical theory.
We study an inflationary scenario with a vector impurity. We show that the universe undergoes anisotropic inflationary expansion due to a preferred direction determined by the vector. Using the slow-roll approximation, we find a formula to determine anisotropy of the inflationary universe. We discuss possible observable predictions of this scenario. In particular, it is stressed that primordial gravitational waves can be induced from curvature perturbations. Hence, even in low scale inflation, a sizable amount of primordial gravitational waves may be produced during inflation.
In the inflationary universe scenario, the physical wavelength of cosmological fluctuation modes which are currently probed in observations was shorter than the Hubble radius, and in fact shorter than the Planck and string lengths, at the beginning of the period of inflation. Thus, during the early stages of evolution, the fluctuations are subject to Planck scale physics. In the context of an inflationary cosmological background, we examine the signatures of a specific modified dispersion relation motivated by the T-duality symmetry of string theory on the power spectrum of gravitational waves…
