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A Planck scale inflationary era -- in a quantum gravity theory predicting discreteness of quantum geometry at the fundamental scale -- produces the scale invariant spectrum of inhomogeneities with very small tensor-to-scalar ratio of perturbations and a hot big bang leading to a natural dark matter genesis scenario. Here we evoke the possibility that some of the major puzzles in cosmology would have an explanation rooted in quantum gravity.

The traditional presentation of Unimodular Gravity (UG) consists on indicating that it is an alternative theory of gravity that restricts the generic diffeomorphism invariance of General Relativity. In particular, as often encountered in the literature, unlike General Relativity, Unimodular Gravity is invariant solely under volume-preserving diffeomorphisms. That characterization of UG has led to some confusion and incorrect statements in various treatments on the subject. For instance, sometimes it is claimed (mistakenly) that only spacetime metrics such that $|$det $g_{\mu \nu}| = 1$ can be considered as valid solutions of the theory. Additionally, that same (incorrect) statement is often invoked to argue that some particular gauges (e.g. the Newtonian or synchronous gauge) are not allowed when dealing with cosmological perturbation theory in UG. The present article is devoted to clarify those and other misconceptions regarding the notion of diffeomorphism invariance, in general, and its usage in the context of UG, in particular., Comment: 26 pages, 2 figures, references updated. Version accepted for publication

We calculate the primordial power spectrum of tensor perturbations, within the emergent universe scenario, incorporating a version of the Continuous Spontaneous Localization (CSL) model as a mechanism capable of: breaking the initial symmetries of the system, generating the perturbations, and also achieving the quantum-to-classical transition of such perturbations. We analyze how the CSL model modifies the characteristics of the B-mode CMB polarization power spectrum, and we explore their differences with current predictions from the standard concordance cosmological model. We have found that, regardless of the CSL mechanism, a confirmed detection of primordial B-modes that fits to a high degree of precision the shape of the spectrum predicted from the concordance $\Lambda$CDM model, would rule out one of the distinguishing features of the emergent universe. Namely, achieving a best fit to the data consistent with the suppression observed in the low multipoles of the angular power spectrum of the temperature anisotropy of the CMB. On the contrary, a confirmed detection that accurately exhibits a suppression of the low multipoles in the B-modes, would be a new feature that could be considered as a favorable evidence for the emergent scenario. In addition, we have been able to establish an upper bound on the collapse parameter of the specific CSL model used., Comment: 13 pages, 3 figures, 1 Appendix. Improved version with additional comments and details. Accepted in EPJC

In this work we analyze how the spectrum of primordial scalar perturbations is modified, within the emergent universe scenario, when a particular version of the Continuous Spontaneous Localization (CSL) model is incorporated as the generating mechanism of initial perturbations, providing also an explanation to the quantum-to-classical transition of such perturbations. On the other hand, a phase of super-inflation, prior to slow-roll inflation, is a characteristic feature of the emergent universe hypothesis. In recent works, it was shown that the super-inflation phase could generically induce a suppression of the temperature anisotropies of the CMB at large angular scales. We study here under what conditions the CSL maintains or modifies these characteristics of the emergent universe and their compatibility with the CMB observations., Comment: 15 pages, 5 figures. Some references added. Version accepted in EPJC

We propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory., Comment: 18 pages, 2 Appendices. Improved version, accepted in EPJC

In this work we consider a wide variety of alternatives opened when applying the continuous spontaneous localization (CSL) dynamical collapse theory to the inflationary era. The definitive resolution of many of the issues discussed here will have to await, not only for a general relativistic CSL theory, but for a fully workable theory of quantum gravity. Our concern here is to explore these issues, and to warn against premature conclusions. This exploration includes: two different approaches to deal with quantum field theory and gravitation, the identification of the collapse-generating operator and the general nature and values of the parameters of the CSL theory. All the choices connected with these issues have the potential to dramatically alter the conclusions one can draw. We also argue that the incompatibilities found in a recent paper, between the CSL parameter values and the CMB observational data, are associated with specific choices made for the extrapolation to the cosmological context of the CSL theory (as it is known to work in non-relativistic laboratory situations) which do not represent the most natural ones., Comment: 13 pages, 1 Appendix. Minor changes in title and abstract

Why is it interesting to try to understand the origin of the universe? Everything we observe today, including our existence, arose from that event. Although we still do not have a theory that allows us to describe the origin itself, the study of the very early era of the universe involves the ideal terrain to analyze the interface between two of today's most successful physical theories, General Relativity and Quantum physics. But it is also an area in which we have a large number of observational data to test our theoretical ideas. Two of the fathers of Quantum physics, Niels Bohr and Werner Heisenberg, shared some thoughts that could be described with these words: "Quantum physics tells us that there is a line between the observed and the observer, and therefore science should be limited to what is observed. We must give up a complete, objective and realistic theory of the world". This article will orbit around these ideas and summarizes how it is that today, from recent works, we are in a position to try to challenge them (at least in part) through cosmology, seeking the quantum description of the early universe., Comment: 9 pages

In a recent paper [J. Martin and V. Vennin, Phys. Rev. Lett. 124, 080402 (2020)] it was argued that, for most natural choices, the direct application of the continuous spontaneous localization (CSL) theory to the inflationary case, as it is known to work in non-relativistic laboratory situations, is ruled out by cosmological observational data, thus casting a shadow on models based on CSL theory. We point out that such results are based on the consideration of a rather narrow set of choices for the application of the theory to the cosmological context and that the landscape of open and different possibilities is extremely vast., Comment: 2 pages

Recently it has been argued that a correct reading of the quantum fluctuations of the vacuum could lead to a solution to the cosmological constant problem. In this work we critically examine such a proposal, finding it questionable due to conceptual and self-consistency problems, as well as issues with the actual calculations. We conclude that the proposal is inadequate as a solution to the cosmological constant problem., Comment: 12 pages. Minor changes, comments added in Conclusions and new references. Accepted for publication in EPJC

In this paper we present a procedure which allows to transform a subset $A$ of $\mathbb{Z}_{p}$ into a set $ A'$ such that $ |2\hspace{0.15cm}\widehat{} A'|\leq|2\hspace{0.15cm}\widehat{} A | $, where $2\hspace{0.15cm}\widehat{} A$ is defined to be the set $\left\{a+b:a\neq b,\;a,b\in A\right\}$. From this result, we get some lower bounds for $ |2\hspace{0.15cm}\widehat{} A| $. Finally, we give some remarks related to the problem for which sets $A\subset \mathbb{Z}_{p}$ we have the equality $|2\hspace{0.15cm}\widehat{} A|=2|A|-1$., Comment: 16 pages

From the first observations made by Slipher, our understanding and interpretation of the cosmological redshift was evolving until reaching the current consensus, through the expanding universe and the emergence of modern physical cosmology within the framework of General Relativity. The redshift is one of the most basic concepts of astronomy, and is one of the few observational parameters that can be measured directly. To refer to the temporal evolution of objects or cosmic structures in the universe, we often do so indistinctly through cosmic time or cosmological redshift. But repeatedly this connection ends up generating confusion not only among popular science communicators but also within the professional astronomical community. In this article, we will make a pedagogical approach to the link between cosmic time and cosmological redshift, and we will also clarify several common misunderstandings around this relation., Comment: 7 pages, 6 figures. Some changes, comments and references added

Within the framework of inflationary models that incorporate a spontaneous reduction of the wave function for the emergence of the seeds of cosmic structure, we study the effects on the primordial scalar power spectrum by choosing a novel initial quantum state that characterizes the perturbations of the inflaton. Specifically, we investigate under which conditions one can recover an essentially scale free spectrum of primordial inhomogeneities when the standard Bunch-Davies vacuum is replaced by another one that minimizes the renormalized stress-energy tensor via a Hadamard procedure. We think that this new prescription for selecting the vacuum state is better suited for the self-induced collapse proposal than the traditional one in the semiclassical gravity picture. We show that the parametrization for the time of collapse, considered in previous works, is maintained. Also, we obtain an angular spectrum for the CMB temperature anisotropies consistent with the one that best fits the observational data. Therefore, we conclude that the collapse mechanism might be of a more fundamental character than previously suspected., Comment: 17 pages, 2 figures. Extended and revised version. To appear in Physics Letters B

In recent years, some studies have drawn attention to the lack of large-angle correlations in the observed cosmic microwave background (CMB) temperature anisotropies with respect to that predicted within the standard $\Lambda$CDM model. Lately, it has been argued that such a lack of correlations could be explained in the framework of the so-called $R_h=ct$ model without inflation. The aim of this work is to study whether there is a mechanism to generate, through a quantum field theory, the primordial power spectrum presented by these authors. Specifically, we consider two different scenarios: first, we assume a scalar field dominating the early Universe in the $R_h=ct$ cosmological model, and second, we deal with the possibility of adding an early inflationary phase to the mentioned model. During the analysis of the consistency between the predicted and observed amplitudes of the CMB temperature anisotropies in both scenarios, we run into deep issues which indicate that it is not clear how to characterize the primordial quantum perturbations within the $R_h=ct$ model., Comment: 14 pages. Final version, improved with additional comments. To appear in EPJC

The Continuous Spontaneous Localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schr\"{o}dinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the parameters characterizing the primordial spectra (scalar and tensor), i.e. the amplitude, the spectral index and the tensor-to-scalar ratio. We found that there exist CSL parameter values, allowed by other non-cosmological experiments, for which our predictions for the angular power spectrum of the CMB temperature anisotropy are consistent with the best fit canonical model to the latest data released by the Planck Collaboration., Comment: 27 pages, including 6 figures, 2 tables and one Appendix. Final version. Accepted in EPJC

The inflationary paradigm is the most successful model that explains the observed spectrum of primordial perturbations. However, the precise emergence of such inhomogeneities and the quantum-to-classical transition of the perturbations has not yet reached a consensus among the community. The Continuous Spontaneous Localization model (CSL), in the cosmological context, might be used to provide a solution to the mentioned issues by considering a dynamical reduction of the wave function. The CSL model has been applied to the inflationary universe before and different conclusions have been obtained. In this letter, we use a different approach to implement the CSL model during inflation. In particular, in addition to accounting for the quantum-to-classical transition, we use the CSL model to generate the primordial perturbations, that is, the dynamical evolution provided by the CSL model is responsible for the transition from a homogeneous and isotropic initial state to a final one lacking such symmetries. Our approach leads to results that can be clearly distinguished from preceding works. Specifically, the scalar and tensor power spectra are not time-dependent, and retains the amplification mechanism of the CSL model. Moreover, our framework depends only on one parameter (the CSL parameter) and its value is consistent with cosmological and laboratory observations., Comment: 14 pages. Final version. To be published in EPJC

The inflationary paradigm is an important cornerstone of the concordance cosmological model. However, standard inflation cannot fully address the transition from an early homogeneous and isotropic stage, to another one lacking such symmetries corresponding to our present universe. In previous works, a self-induced collapse of the wave function has been suggested as the missing ingredient of inflation. Most of the analysis regarding the collapse hypothesis has been solely focused on the characteristics of the spectrum associated to scalar perturbations, and within a semiclassical gravity framework. In this Letter, working in terms of a joint metric-matter quantization for inflation, we calculate, for the first time, the tensor power spectrum and the tensor-to-scalar ratio corresponding to the amplitude of primordial gravitational waves resulting from considering a generic self-induced collapse., Comment: 10 pages. Improved version. Replaced to match version to be published in Phys. Lett. B

In this work, we consider the problem of the emergence of seeds of cosmic structure in the framework of the non-inflationary model proposed by Hollands and Wald. In particular, we consider a modification to that proposal designed to account for breaking the symmetries of the initial quantum state, leading to the generation of the primordial inhomogeneities. This new ingredient is described in terms of a spontaneous reduction of the wave function. We investigate under which conditions one can recover an essentially scale free spectrum of primordial inhomogeneities, and which are the dominant deviations that arise in the model as a consequence of the introduction of the collapse of the quantum state into that scenario., Comment: 10 pages. Comments added. Replaced to match version to be published in PLB

In this work, we show that when supernova Ia (SN Ia) data sets are used to put constraints on the free parameters of inhomogeneous models, certain extra information regarding the light-curve fitter used in the supernovae Ia luminosity fluxes processing should be taken into account. We found that the size of the void as well as other parameters of these models might be suffering extra degenerations or additional systematic errors due to the fitter. A recent proposal to relieve the tension between the results from Planck satellite and SNe Ia is re-analyzed in the framework of these subjects., Comment: 9 pages, 5 figures. Corrected typos, comments added, replaced to match version to be published in Phys. Lett. B

We construct an operational calculus supported on the algebraic operational calculus introduced by Bengochea and Verde. With this operational calculus we study the solution of certain Bessel type equations., Comment: 10 pages

Cosmological distances inferred from supernova Ia observations constitute the most direct and solid evidence for the recently detected accelerated expansion of the universe. In this contribution, we show some inconsistencies between two of the main light-curve fitters used for the elaboration of supernova Ia data sets, opening new observational challenges regarding the use of these luminosity distances when combined with CMB and BAO data. We also mention ongoing analysis related to alternative models. The resolution of these challenges will be crucial for XXI century cosmology., Comment: 4 pages, 3 figures. Submitted to the BAAA Vol. 55, 2012

We show that when a procedure is made to remove the tension between a supernova Ia (SN Ia) data set and observations from BAO and CMB, there might be the case where the same SN Ia set built with two different light-curve fitters behaves as two separate and distinct supernova sets, and the tension found by some authors between supernova sets actually could be due to tension or inconsistency between fitters. We also show that the information of the fitter used in an SN Ia data set could be relevant to determine whether phantom type models are favored or not when such a set is combined with the BAO/CMB joint parameter., Comment: 8 pages, 7 figures and 2 tables. Improved version. Accepted in Phys. Lett. B

In the present work we analyze and compare the information coming from different observational data sets in the context of a sort of f(T) theories. We perform a joint analysis with measurements of the most recent type Ia supernovae (SNe Ia), Baryon Acoustic Oscillation (BAO), Cosmic Microwave Background radiation (CMB), Gamma-Ray Bursts data (GRBs) and Hubble parameter observations (OHD) to constraint the only new parameter these theories have. It is shown that when the new combined BAO/CMB parameter is used to put constraints, the result is different from previous works. We also show that when we include Observational Hubble Data (OHD) the simpler LambdaCDM model is excluded to one sigma level, leading the effective equation of state of these theories to be of phantom type. Also, analyzing a tension criterion for SNe Ia and other observational sets, we obtain more consistent and better suited data sets to work with these theories., Comment: 8 pages, 4 figures. AIC criterion added. Version accepted in Phys. Lett. B

It is shown that the recently detected acceleration of the universe can be understood by considering a modification of the teleparallel equivalent of General Relativity (TEGR), with no need of dark energy. The solution also exhibits phases dominated by matter and radiation as expected in the standard cosmological evolution. We perform a joint analysis with measurements of the most recent type Ia supernovae (SNe Ia), Baryon Acoustic Oscillation (BAO) peak and estimates of the CMB shift parameter data to constraint the only new parameter this theory has., Comment: 5 pages, 5 figures, replaced to match version to be published in Physical Review D

We show exact solutions of Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of Born-Infeld equations generates an interaction between background and wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction --a behavior resembling the one of a wave in an anisotropic medium--. This feature could open up a way to experimental tests of Born-Infeld theory., Comment: 4 pages, Revtex4, 1 figure, corrected typos, comments clarified, version accepted for publication

Born-Infeld electromagnetic waves interacting with a static magnetic background are studied in an expanding universe. The non-linear character of Born-Infeld electrodynamics modifies the relation between the energy flux and the distance to the source, which gains a new dependence on the redshift that is governed by the background field. We compute the luminosity distance as a function of the redshift and compare with Maxwellian curves for supernovae type Ia., Comment: 7 Pages, 4 figures. Extended introduction and some clarifications in sections 2 and 3. Version to be published in JCAP