We study the implications of the recently proposed Trans-Planckian censorship conjecture (TCC) for early Universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than ${10}^9\mathrm{GeV}$. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter $\epsilon$ of the model to be very small ($<{10}^{-31}$). This leads to the prediction of a negligible amplitude of primordial gravitational waves. For slow-roll inflation models, it also leads to severe fine-tuning of initial conditions.

It has recently been shown that a Hagedorn phase of string gas cosmology can provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. In this Letter, we compute the spectrum of tensor metric fluctuations (gravitational waves) in this scenario and show that it is also nearly scale invariant. However, whereas the spectrum of scalar modes has a small red tilt, the spectrum of tensor modes has a small blue tilt, unlike what occurs in slow-roll inflation. This provides a possible observational way to distinguish between our cosmological scenario and conventional slow-roll inflation.

In this article, we study the implications of string swampland criteria for dark energy in view of ongoing and future cosmological observations. If string theory should be the ultimate quantum gravity theory, there is evidence that exact de Sitter solutions with a positive cosmological constant cannot describe the fate of the late-time universe. Even though cosmological models with dark energy given by a scalar field $\pi$ evolving in time are not in direct tension with string theory, they have to satisfy the swampland criteria $|\mathrm{\Delta }\pi |<d\sim \mathcal{O}(1)$ and $|V^{\prime }|/V>c\sim \mathcal{O}(1)$, where $V$ is the scalar field potential. In view of the restrictive implications that the swampland criteria have on dark energy, we investigate the accuracy needed for future observations to tightly constrain standard dark-energy models. We find that current $3\text{−}\sigma$ constraints with $c\lesssim 1.35$ are still well in agreement with the string swampland criteria. However, stage-4 surveys such as Euclid, LSST, and DESI, tightly constraining the equation of state $w(z)$, will start putting surviving quintessence models into tensions with the string swampland criteria by demanding $c<0.4$. We further investigate whether any idealized futuristic survey will ever be able to give a decisive answer to the question whether the cosmological constant would be preferred over a time-evolving dark-energy model within the swampland criteria. Hypothetical surveys with a reduction in the uncertainties by a factor of $\sim 20$ compared to Euclid would be necessary to reveal strong tension between quintessence models obeying the string swampland criteria and observations by pushing the allowed values down to $c<0.1$. In view of such perspectives, there will be fundamental observational limitations with future surveys.

We re-examine the non-singular Matter Bounce scenario first developed in [20], which starts with a matter-dominated period of contraction and transitions into an Ekpyrotic phase of contraction. We consider both matter fields, the first of which plays the role of regular matter, and the second of which is responsible for the non-singular bounce. Since the dominant matter field is massive, the induced curvature fluctuations are initially not scale-invariant, whereas the fluctuations of the second scalar field (which are initially entropy fluctuations) are scale-invariant. We study the transfer of the initial entropy perturbations into curvature fluctuations in the matter-dominated phase of contraction and show that the latter become nearly scale invariant on large scales but are blue tilted on small scales. We study the evolution of both curvature and entropy fluctuations through the bounce, and show that both have a scale-invariant spectrum which is blue-tilted on small scales. However, we find that the entropy fluctuations have an amplitude that is much smaller than that of the curvature perturbations, due to gravitational amplification of curvature perturbations during the bounce phase.

A nonsingular bouncing cosmology in which the scales of interest today exit the Hubble radius in a matter-dominated contracting phase yields an alternative to inflation for producing a scale-invariant spectrum of adiabatic cosmological fluctuations. In this paper we identify signatures in the non-Gaussianities of the fluctuations which are specific to this scenario and allow it to be distinguished from the results of inflationary models.