EDP - Equacions en Derivades Parcials i Aplicacions
http://hdl.handle.net/2117/79726
Thu, 18 Aug 2022 02:45:03 GMT2022-08-18T02:45:03ZCosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies
http://hdl.handle.net/2117/367803
Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies
Abdalla, Elcio; Abellan, Guillermo Franco; Aboubrahim, Amin; Agnello, Adriano; Akarsu, Özgür; Akrami, Yashar; Alestas, George; Aloni, Daniel; Amendola, Luca; Anchordoqui, Luis A.; Haro Cases, Jaume
The standard ¿ Cold Dark Matter (¿CDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant , the – tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the tension between the Planck CMB estimate of the Hubble constant and the SH0ES collaboration measurements. After showing the evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density , and the amplitude or rate of the growth of structure (). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the – tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions
Fri, 27 May 2022 12:14:34 GMThttp://hdl.handle.net/2117/3678032022-05-27T12:14:34ZAbdalla, ElcioAbellan, Guillermo FrancoAboubrahim, AminAgnello, AdrianoAkarsu, ÖzgürAkrami, YasharAlestas, GeorgeAloni, DanielAmendola, LucaAnchordoqui, Luis A.Haro Cases, JaumeThe standard ¿ Cold Dark Matter (¿CDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant , the – tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the tension between the Planck CMB estimate of the Hubble constant and the SH0ES collaboration measurements. After showing the evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density , and the amplitude or rate of the growth of structure (). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the – tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questionsTopics in cosmology — clearly explained by means of simple examples
http://hdl.handle.net/2117/366576
Topics 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
Fri, 29 Apr 2022 08:58:38 GMThttp://hdl.handle.net/2117/3665762022-04-29T08:58:38ZHaro 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 inflation
http://hdl.handle.net/2117/362823
Understanding 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
Tue, 22 Feb 2022 09:23:03 GMThttp://hdl.handle.net/2117/3628232022-02-22T09:23:03ZHaro 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 inflation
http://hdl.handle.net/2117/362538
A 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
Thu, 17 Feb 2022 09:18:18 GMThttp://hdl.handle.net/2117/3625382022-02-17T09:18:18ZHaro 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 kernels
http://hdl.handle.net/2117/361251
Pointwise 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.
Tue, 01 Feb 2022 13:52:33 GMThttp://hdl.handle.net/2117/3612512022-02-01T13:52:33ZAlonso 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 constraints
http://hdl.handle.net/2117/352892
Quintessential 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
Fri, 01 Oct 2021 11:20:20 GMThttp://hdl.handle.net/2117/3528922021-10-01T11:20:20ZAresté 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 points
http://hdl.handle.net/2117/352747
Discrepancy 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.
Thu, 30 Sep 2021 11:52:50 GMThttp://hdl.handle.net/2117/3527472021-09-30T11:52:50ZMas 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 supergravity
http://hdl.handle.net/2117/352204
a-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
Fri, 24 Sep 2021 11:54:50 GMThttp://hdl.handle.net/2117/3522042021-09-24T11:54:50ZAresté 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 scenarios
http://hdl.handle.net/2117/352196
Theoretical 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...
Fri, 24 Sep 2021 08:19:34 GMThttp://hdl.handle.net/2117/3521962021-09-24T08:19:34ZYang, 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 curvature
http://hdl.handle.net/2117/347751
Near-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
Tue, 22 Jun 2021 10:29:42 GMThttp://hdl.handle.net/2117/3477512021-06-22T10:29:42ZCabré 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.