Exit from Inflation with a First-Order Phase Transition and a Gravitational Wave Blast

In double-field inflation, which exploits two scalar fields, one of the fields rolls slowly during inflation whereas the other field is trapped in a meta-stable vacuum. The nucleation rate from the false vacuum to the true one becomes substantial enough that triggers a first order phase transition and ends inflation. We revisit the question of first order phase transition in an "extended" model of hybrid inflation, realizing the double-field inflationary scenario, and correctly identify the parameter space that leads to a first order phase transition at the end of inflation. We compute the gravitational wave profile which is generated during this first order phase transition. Assuming instant reheating, the peak frequency falls in the $1$ GHz to $10$ GHz frequency band and the amplitude varies in the range $10^{-11}\lesssim \Omega_{\rm GW} h^2 \lesssim 10^{-8}$, depending on the value of the cosmological constant in the false vacuum. The signature could be observed by the planned Chongqing high frequency gravitational probe. For a narrow band of vacuum energies, the first order phase transition can happen after the end of inflation via the violation of slow-roll, with a peak frequency that varies from $1$ THz to $100$ THz. For smaller values of cosmological constant, even though inflation can end via slow-roll violation, the universe gets trapped in a false vacuum whose energy drives a second phase of eternal inflation. This range of vacuum energies do not lead to viable inflationary models, unless the value of the cosmological constant is compatible with the observed value, $M\sim 10^{-3}$ eV.Comment: v1: 15 pages, 8 Figures; v2: typos corrected;v3: matched the PLB versio

Rescuing Single Field Inflation from the Swampland

The difficulty of building metastable vacua in string theory has led some to conjecture that, in the string theory landscape, potentials satisfy $\left|\nabla V/V\right|\geq c\sim \mathcal{O}(1)$. This condition, which is supported by different explicit constructions, suggests that the EFTs which lead to metastable de-Sitter vacua belong to what is dubbed as swampland. This condition endangers the paradigm of single field inflation. In this paper, we show how scalar excited initial states cannot rescue single field inflation from the swampland, as they produce large local scalar non-gaussianity, which is in conflict with the Planck upper bound. Instead, we demonstrate that one can salvage single field inflation using excited initial states for tensor perturbations, which in this case produce only large flattened non-gaussianity in the tensor bispectrum. We comment on the possible methods one can prepare such excited initial conditions for the tensor perturbations.Comment: v1: 8 pages double columns, no figures; v2: references added, matched the PLB versio

A Note on Calm Excited States of Inflation

We identify a two-parameter family of excited states within slow-roll inflation for which either the corrections to the two-point function or the characteristic signatures of excited states in the three-point function -- i.e. the enhancement for the flattened momenta configurations-- are absent. These excited states may nonetheless violate the adiabaticity condition maximally. We dub these initial states of inflation calm excited states. We show that these two sets do not intersect, i.e., those that leave the power-spectrum invariant can be distinguished from their bispectra, and vice versa. The same set of calm excited states that leave the two-point function invariant for slow-roll inflation, do the same task for DBI inflation. However, at the level of three-point function, the calm excited states whose flattened configuration signature is absent for slow-roll inflation, will lead to an enhancement for DBI inflation generally, although the signature is smaller than what suggested by earlier analysis. This example also illustrates that imposing the Wronskian condition is important for obtaining a correct estimate of the non-Gaussian signatures.Comment: v1: 13 pages; v2: matched the JCAP versio

Observing the Structure of the Landscape with the CMB Experiments

Assuming that inflation happened through a series of tunneling in the string theory landscape, it is argued that one can determine the structure of vacua using precise measurements of the scalar spectral index and tensor perturbations at large scales. It is shown that for a vacuum structure where the energy gap between the minima is constant, i.e. $\epsilon_i=i m_f^4$, one obtains the scalar spectral index, $n_s$, to be $\simeq 0.9687$, for the modes that exit the horizon 60 e-folds before the end of inflation. Alternatively, for a vacuum structure in which the energy gap increases linearly with the vacuum index, i.e. $\epsilon_i=\frac{i^2}{2} m_f^4$, $n_s$ turns out to be $\simeq 0.9614$. Both these two models are motivated within the string theory landscape using flux-compactification and their predictions for scalar spectral index are compatible with WMAP results. For both these two models, the results for the scalar spectral index turn out to be independent of $m_f$. Nonetheless, assuming that inflation started at Planckian energies and that there had been successful thermalization at each step, one can constrain $m_f<2.6069\times 10^{-5} m_P$ and $m_f<6.5396\times 10^{-7} m_P$ in these two models, respectively. Violation of the single-field consistency relation between the tensor and scalar spectra is another prediction of chain inflation models. This corresponds to having a smaller tensor/scalar ratio at large scales in comparison with the slow-roll counterparts. Similar to slow-roll inflation, it is argued that one can reconstruct the vacuum structure using the CMB experiments.Comment: v1: 8 pages, 2 figures; v2: grammatical typos corrected, results unchanged v3: To be published in JCA

Black Holes as Beads on Cosmic Strings

We consider the possibility of formation of cosmic strings with black holes as beads. We focus on the simplest setup where two black holes are formed on a long cosmic string. It turns out the in absence of a background magnetic field and for observationally viable values for cosmic string tensions, $\mu<2\times 10^{-7}$, the tension of the strut in between the black holes has to be less than the ones that run into infinity. This result does not change if a cosmological constant is present. However if the background magnetic field is turned on, we can have stable setups where the tensions of all cosmic strings are equal. We derive the equilibrium conditions in each of these setups depending on whether the black holes are extremal or non-extremal. We obtain cosmologically acceptable solutions with solar mass black holes and intragalactic strength cosmic magnatic field.Comment: v1: 1+13 pages, 1 figure; v2: References added, typos corrected; v3: Matched the published versio

Gauged M-flation After BICEP2

In view of the recent BICEP2 results [arXiv:1403.3985] which may be attributed to the observation of B-modes polarization of the CMB with tensor-to-scalar ratio $r=0.2_{-0.05}^{+0.07}$, we revisit M-flation model. Gauged M-flation is a string theory motivated inflation model with Matrix valued scalar inflaton fields in the adjoint representation of a $U(N)$ Yang-Mills theory. In continuation of our previous works, we show that in the M-flation model induced from a supersymmetric 10d background probed by a stack of $N$ D3-branes, the "effective inflaton" $\phi$ has a double-well Higgs-like potential, with minima at $\phi=0,\mu$. We focus on the $\phi>\mu$, symmetry-breaking region. We thoroughly examine predictions of the model for $r$ in the $2\sigma$ region allowed for $n_S$ by the Planck experiment. As computed in [arXiv:0903.1481], for $N_e=60$ and $n_S=0.96$ we find $r\simeq 0.2$, which sits in the sweet spot of BICEP2 region for $r$. We find that with increasing $\mu$ arbitrarily, $n_S$ cannot go beyond $\simeq 0.9670$. As $n_S$ varies in the $2\sigma$ range which is allowed by Planck and could be reached by the model, $r$ varies in the range $[0.1322,0.2623]$. Future cosmological experiments, like the CMBPOL, that confines $n_S$ with $\sigma(n_S)=0.0029$ can constrain the model further. Also, in this region of potential, for $n_S=0.9603$, we find that the largest isocurvature mode, which is uncorrelated with curvature perturbations, has a power spectrum with the amplitude of order $10^{-11}$ at the end of inflation. We also discuss the range of predictions of $r$ in the hilltop region, $\phi< \mu$.Comment: v1:16 pages, 9 figures; v2: matched the published versio

Matrix Inflation and the Landscape of its Potential

Recently we introduced an inflationary setup in which the inflaton fields are matrix valued scalar fields with a generic quartic potential, M-flation. In this work we study the landscape of various inflationary models arising from M-flation. The landscape of the inflationary potential arises from the dynamics of concentric multiple branes in appropriate flux compactifications of string theory. After discussing the classical landscape of the theory we study the possibility of transition among various inflationary models appearing at different points on the landscape, mapping the quantum landscape of M-flation. As specific examples, we study some two-field inflationary models arising from this theory in the landscape.Comment: v1: 34 pages, 5 figures; v2: To be published in JCAP; v3: JCAP versio

On the Tensor/Scalar Ratio in Inflation with UV Cutoff

Anisotropy of the cosmic microwave background radiation (CMB) originates from both tensor and scalar perturbations. To study the characteristics of each of these two kinds of perturbations, one has to determine the contribution of each to the anisotropy of CMB. For example, the ratio of the power spectra of tensor/scalar perturbations can be used to tighten bounds on the scalar spectral index. We investigate here the implications for the tensor/scalar ratio of the recent discovery (noted in astro-ph/0410139) that the introduction of a minimal length cutoff in the structure of spacetime does not leave boundary terms invariant. Such a cutoff introduces an ambiguity in the choice of action for tensor and scalar perturbations, which in turn can affect this ratio. We numerically solve for both tensor and scalar mode equations in a near-de-sitter background and explicitly find the cutoff dependence of the tensor/scalar ratio during inflation.Comment: 19 pages, 14 figures, to appear in Nucl. Phys. B; v4: typos corrected, matched with the published versio