EDP - Equacions en Derivades Parcials i Aplicacionshttp://hdl.handle.net/2117/797262022-05-19T17:50:05Z2022-05-19T17:50:05ZTopics in cosmology — clearly explained by means of simple examplesHaro Cases, JaumeElizalde Rius, Emiliohttp://hdl.handle.net/2117/3665762022-05-17T10:48:15Z2022-04-29T08:58:38ZTopics in cosmology — clearly explained by means of simple examples
Haro Cases, Jaume; Elizalde Rius, Emilio
This is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called a-attractors in the context of quintessential inflation
2022-04-29T08:58:38ZHaro Cases, JaumeElizalde Rius, EmilioThis is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called a-attractors in the context of quintessential inflationUnderstanding gravitational particle production in quintessential inflationHaro Cases, JaumePan, SupriyaAresté Saló, Lliberthttp://hdl.handle.net/2117/3628232022-02-27T15:25:53Z2022-02-22T09:23:03ZUnderstanding gravitational particle production in quintessential inflation
Haro Cases, Jaume; Pan, Supriya; Aresté Saló, Llibert
The diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regime
2022-02-22T09:23:03ZHaro Cases, JaumePan, SupriyaAresté Saló, LlibertThe diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regimeA review of quintessential inflationHaro Cases, JaumeAresté Saló, Lliberthttp://hdl.handle.net/2117/3625382022-05-17T12:53:28Z2022-02-17T09:18:18ZA review of quintessential inflation
Haro Cases, Jaume; Aresté Saló, Llibert
Some of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preserved
2022-02-17T09:18:18ZHaro Cases, JaumeAresté Saló, LlibertSome of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preservedPointwise monotonicity of heat kernelsAlonso Orán, DiegoChamizo, FernandoMartínez Martínez, Ángel DavidMas Blesa, Alberthttp://hdl.handle.net/2117/3612512022-02-06T15:49:28Z2022-02-01T13:52:33ZPointwise monotonicity of heat kernels
Alonso Orán, Diego; Chamizo, Fernando; Martínez Martínez, Ángel David; Mas Blesa, Albert
In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.
2022-02-01T13:52:33ZAlonso Orán, DiegoChamizo, FernandoMartínez Martínez, Ángel DavidMas Blesa, AlbertIn this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.Quintessential inflation and cosmological seesaw mechanism: reheating and observational constraintsAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, Jaumehttp://hdl.handle.net/2117/3528922022-05-17T10:16:27Z2021-10-01T11:20:20ZQuintessential inflation and cosmological seesaw mechanism: reheating and observational constraints
Aresté Saló, Llibert; Benistry, David; Guendelman, Eduardo I.; Haro Cases, Jaume
Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of a-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a cosmological seesaw mechanism (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. Here we show that the model agrees with the recent observations and with the reheating constraints. Therefore the model gives a reasonable scenario beyond the standard ¿CDM that includes the inflationary epoch
2021-10-01T11:20:20ZAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, JaumeRecently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of a-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a cosmological seesaw mechanism (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. Here we show that the model agrees with the recent observations and with the reheating constraints. Therefore the model gives a reasonable scenario beyond the standard ¿CDM that includes the inflationary epochDiscrepancy of minimal riesz energy pointsMas Blesa, AlbertMarzo Sánchez, Jordihttp://hdl.handle.net/2117/3527472022-04-08T00:28:56Z2021-09-30T11:52:50ZDiscrepancy of minimal riesz energy points
Mas Blesa, Albert; Marzo Sánchez, Jordi
We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in S2 were obtained. Our result improves previously known bounds for 0=s<2 and s¿1 in S2, where s=0 is Wolff’s result, and for d-t0<s<d with t0˜2.5 when d=3 and s¿d-1.
2021-09-30T11:52:50ZMas Blesa, AlbertMarzo Sánchez, JordiWe find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in S2 were obtained. Our result improves previously known bounds for 0=s<2 and s¿1 in S2, where s=0 is Wolff’s result, and for d-t0<s<d with t0˜2.5 when d=3 and s¿d-1.a-attractors in quintessential inflation motivated by supergravityAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, Jaumehttp://hdl.handle.net/2117/3522042022-05-17T10:40:25Z2021-09-24T11:54:50Za-attractors in quintessential inflation motivated by supergravity
Aresté Saló, Llibert; Benistry, David; Guendelman, Eduardo I.; Haro Cases, Jaume
An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of a-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a zero-vacuum energy density at late times. However, in this paper, we disregard this cosmological constant, showing that the obtained results are very close to the ones obtained recently in the context of Lorentzian quintessential inflation and thus depicting with great accuracy the early- and late-time acceleration of our Universe. The model is compatible with the recent observations. Finally, we review the treatment of the a-attractor and we show that our potential depicts the late time cosmic acceleration with an effective equation of state equal to -1
2021-09-24T11:54:50ZAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, JaumeAn exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of a-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a zero-vacuum energy density at late times. However, in this paper, we disregard this cosmological constant, showing that the obtained results are very close to the ones obtained recently in the context of Lorentzian quintessential inflation and thus depicting with great accuracy the early- and late-time acceleration of our Universe. The model is compatible with the recent observations. Finally, we review the treatment of the a-attractor and we show that our potential depicts the late time cosmic acceleration with an effective equation of state equal to -1Theoretical and observational bounds on some interacting vacuum energy scenariosYang, WeiqiangPan, SupriyaAresté Saló, LlibertHaro Cases, Jaumehttp://hdl.handle.net/2117/3521962022-05-17T11:08:55Z2021-09-24T08:19:34ZTheoretical and observational bounds on some interacting vacuum energy scenarios
Yang, Weiqiang; Pan, Supriya; Aresté Saló, Llibert; Haro Cases, Jaume
The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble function is considered and sometimes it is argued that, as the interaction function is a local property, the inclusion of the Hubble function may influence the overall dynamics. This is the starting point of the present article where we consider a very simple interacting cosmic scenario between vacuum energy and the cold dark matter characterized by various interaction functions originated from a general interaction function...
2021-09-24T08:19:34ZYang, WeiqiangPan, SupriyaAresté Saló, LlibertHaro Cases, JaumeThe dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble function is considered and sometimes it is argued that, as the interaction function is a local property, the inclusion of the Hubble function may influence the overall dynamics. This is the starting point of the present article where we consider a very simple interacting cosmic scenario between vacuum energy and the cold dark matter characterized by various interaction functions originated from a general interaction function...Near-sphere lattices with constant nonlocal mean curvatureCabré Vilagut, XavierFall, Mouhamed MoustaphaWeth, Tobiashttp://hdl.handle.net/2117/3477512021-06-28T07:47:32Z2021-06-22T10:29:42ZNear-sphere lattices with constant nonlocal mean curvature
Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Weth, Tobias
We are concerned with unbounded sets of RN whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter functional under a volume constraint. We construct CNMC sets which are the countable union of a certain bounded domain and all its translations through a periodic integer lattice of dimension M=N. Our CNMC sets form a C2 branch emanating from the unit ball alone and where the parameter in the branch is essentially the distance to the closest lattice point. Thus, the new translated near-balls (or near-spheres) appear from infinity. We find their exact asymptotic shape as the parameter tends to infinity.
The final publication is available at link.springer.com
2021-06-22T10:29:42ZCabré Vilagut, XavierFall, Mouhamed MoustaphaWeth, TobiasWe are concerned with unbounded sets of RN whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter functional under a volume constraint. We construct CNMC sets which are the countable union of a certain bounded domain and all its translations through a periodic integer lattice of dimension M=N. Our CNMC sets form a C2 branch emanating from the unit ball alone and where the parameter in the branch is essentially the distance to the closest lattice point. Thus, the new translated near-balls (or near-spheres) appear from infinity. We find their exact asymptotic shape as the parameter tends to infinity.Discrepancies between observational data and theoretical forecast in single field slow roll inflationAmorós Torrent, JaumeHaro Cases, Jaumehttp://hdl.handle.net/2117/3477422021-06-28T07:46:21Z2021-06-22T10:00:44ZDiscrepancies between observational data and theoretical forecast in single field slow roll inflation
Amorós Torrent, Jaume; Haro Cases, Jaume
The PLANCK collaboration has determined, or greatly constrained, values for the spectral parameters of the CMB radiation, namely the spectral index ns, its running as, the running of the running ßs, using a growing body of measurements of CMB anisotropies by the Planck satellite and other missions. These values do not follow the hierarchy of sizes predicted by single field, slow roll inflationary theory, and are thus difficult to fit for such inflation models. In this work we present first a study of 49 single field, slow roll inflationary potentials in which we assess the likelyhood of these models fitting the spectral parameters to their currently most accurate determination given by the PLANCK collaboration. We check numerically with a MATLAB program the spectral parameters that each model can yield for a very broad, comprehensive list of possible parameter and field values. The comparison of spectral parameter values supported by the models with their determinations by the PLANCK collaboration leads to the conclusion that the data provided by PLANCK2015 TT+lowP and PLANCK2015 TT,TE,EE+lowP taking into account the running of the running disfavours 40 of the 49 models with confidence level at least 92.8 %. Next, we discuss the reliability of the current computations of these spectral parameters. We identify a bias in the method of determination of the spectral parameters by least residue parameter fitting (using MCMC or any other scheme) currently used to reconstruct the power spectrum of scalar perturbations. This bias can explain the observed contradiction between theory and observations. Its removal is computationally costly, but necessary in order to compare the forecasts of single field, slow roll theories with observation
2021-06-22T10:00:44ZAmorós Torrent, JaumeHaro Cases, JaumeThe PLANCK collaboration has determined, or greatly constrained, values for the spectral parameters of the CMB radiation, namely the spectral index ns, its running as, the running of the running ßs, using a growing body of measurements of CMB anisotropies by the Planck satellite and other missions. These values do not follow the hierarchy of sizes predicted by single field, slow roll inflationary theory, and are thus difficult to fit for such inflation models. In this work we present first a study of 49 single field, slow roll inflationary potentials in which we assess the likelyhood of these models fitting the spectral parameters to their currently most accurate determination given by the PLANCK collaboration. We check numerically with a MATLAB program the spectral parameters that each model can yield for a very broad, comprehensive list of possible parameter and field values. The comparison of spectral parameter values supported by the models with their determinations by the PLANCK collaboration leads to the conclusion that the data provided by PLANCK2015 TT+lowP and PLANCK2015 TT,TE,EE+lowP taking into account the running of the running disfavours 40 of the 49 models with confidence level at least 92.8 %. Next, we discuss the reliability of the current computations of these spectral parameters. We identify a bias in the method of determination of the spectral parameters by least residue parameter fitting (using MCMC or any other scheme) currently used to reconstruct the power spectrum of scalar perturbations. This bias can explain the observed contradiction between theory and observations. Its removal is computationally costly, but necessary in order to compare the forecasts of single field, slow roll theories with observation