It is well known that a scalar field dark matter with a quadratic potential undergoes fast oscillations when the time period represented by the mass scale in the Klein-Gordon equation becomes much smaller than that set by the Hubble parameter. This makes a solution to the equation numerically intractable. Many works in the literature have addressed the problem by either switching between solving the Klein-Gordon equation in the well-behaved regime to solving the fluid equations at the onset of oscillations, or by introducing a new set of variables that can absorb these oscillations. Despite being successful, these techniques rely on an estimate of when the oscillations start. For large scale scans of a model's parameter space, this can become cumbersome. Furthermore, the techniques have been used mainly for non-interacting dark matter models. In this work, we introduce an averaging technique with an automatic detection of the onset of oscillations, capable of capturing the non-interacting as well as the interacting dark matter scenarios. The technique, implemented in , is tested on the QCDM model and shows excellent detection and averaging abilities. We also update the cosmological constraints on the model using the most recent public data.

We study supercooled first-order phase transitions in a supersymmetric hidden sector with a spontaneously broken U(1)_X, focusing on the frequency range of the Einstein Telescope and Cosmic Explorer. Along the D-flat direction the tree-level quartic vanishes, so the barrier is generated radiatively by soft SUSY-breaking splittings. In the DR scheme the gaugino mass M_ sets the barrier depth, while the soft scalar mass m_0 stabilizes the broken vacuum. For M_/v_X≃0.05–0.23, the predicted signal reaches Ω_ GWh^2∼3×10^-10 near the percolation boundary. The observable amplitude depends sensitively on the portal coupling δ through the hidden-to-visible temperature ratio at percolation: for a cold initial hidden sector the signal rises from the ET floor at δ=10^-6 to Ω_ GWh^2≃7×10^-11 as the sectors approach thermal contact at δ=10^-4, while a hotter initial hidden sector gives a large signal already for weak portal coupling. We follow this evolution with an 11-variable Boltzmann system that separates the cold nucleating exterior from the reheated true-vacuum interior; reheating mainly enters through the energy budget and redshift factors. The same hidden sector can reproduce Ω_ CDMh^2=0.12 through relativistic dark-quark freeze-out followed by entropy dilution from hidden-Higgs decay, with m_q≃30–800keV and N_ eff≲ few×10^-5.

The recent detection of a gravitational wave background in the nano-Hertz frequency range by Pulsar Timing Array (PTA) collaborations, including NANOGrav, EPTA, and PPTA, has opened a new avenue for exploring fundamental physics in the early universe. In this work, we analyze a supercooled first-order phase transition in a hidden sector with a spontaneously broken U(1)_X gauge symmetry as a source for this signal. We demonstrate that the thermal history of the hidden and visible sectors plays a crucial role in the gravitational wave power spectrum analysis. Our analysis shows that supercooled phase transitions can generate gravitational waves strong enough to explain the PTA observations while satisfying cosmological constraints from Big Bang Nucleosynthesis.

The development in the early seventies of supersymmetry, in the mid-seventies of gauge supersymmetry and supergravity, and in the early eighties of gravity mediated breaking of supersymmetry and of supergravity grand unification have led to remarkable progress in the pursuit of unification of fundamental interactions of particle physics. They have also led to the intertwining of particle physics, cosmology, and strings. Since supersymmetry and supergravity are manifest in the low energy limit of superstring below the Planck scale, experimental test of them are of interest regarding the validity of the superstring itself. For that reason, over the past decades, after the advent of supersymmetry and SUGRA models, there have been sustained experimental searches for supersymmetry at colliders, in precision experiments, and in astrophysical and cosmological data. The SUSY and SUGRA models have also had deep impact on theories related to inflation, dark matter, and dark energy. The purpose of this article is to provide a view from the bridge of these developments over the past fifty years circa 1974-2024.

While ΛCDM provides a good fit to cosmological data, it fails to address many of the outstanding questions in contemporary cosmology. Chief among these are the Hubble tension and the apparent dynamical nature of dark energy as inferred from the recent DESI DR2 analysis. In this work, we analyze a field-theoretic description of cosmology where both dark energy and dark matter are interacting spin zero fields. We give a thorough study of a wide range of the interaction strength and demonstrate the effect on the dark energy equation of state and the Hubble tension. Using the recent cosmological data, we extract constraints on cosmological parameters including the free parameters of the model.

An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the Standard Model where the dark sector consists of dark matter particles charged under a U(1)x gauge symmetry, while a subset of dark fields also carry lepton number but no U(1)x charge. We demonstrate that, with CP violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves the lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Furthermore, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with Tp/mAx << 1, where Tp is the percolation temperature and mAx is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, and PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.

An analysis is given of interacting dark energy and dark matter where the dark energy is assumed to be an ultralight axionic field with a pseudo-Nambu-Goldstone Boson potential which is in general a superposition of N number of cosine terms motivated by supergravity and string models with a U(1) global symmetry, where the symmetry is broken by instanton effects. The case N=2 is investigated in detail and a fit to cosmological data is performed where it is found that a better fit is obtained in comparison with the N=1 case. The fits also constrain high scale parameters, i.e., the axion decay constant which is determined to be sub-Planckian, a result consistent with string theory that disfavors trans-Planckian axion decay constant. Furthermore, the dark energy-dark matter interaction strength is constrained to be feeble, i.e., λ≲ 4× 10^-6 m_ Pl^-2 Mpc^-2. We study possible implications of this type of potential on the Hubble tension and on the dynamics of the dark energy equation of state using the DESI-DR2 data. For the cases N=3,4, the analysis exhibits the phenomenon of transmutation even in the absence of coupling to dark matter, where thawing quintessence transmutes to freezing quintessence. The analysis is internally consistent in its treatment of the dark energy-dark matter interaction as it is based on an underlying Lagrangian, in contrast with several previous works where the sources are chosen in an ad hoc manner to satisfy energy conservation.

The SO(10) model with a heavy Higgs spectrum consisting of 560 + 560 and a light Higgs spectrum consisting of 2 10 + 320 plet representations of SO(10) is unique among SO(10) models. It has the remarkable property that VEVs of 560 and 560 can simultaneously reduce the rank of the gauge group and further reduce the remaining symmetry down to the Standard Model gauge group. Additionally, on mixing with the light fields all the Higgs fields become heavy except for one pair of light Higgs doublets just as in MSSM. This model has not been fully explored thus far because of the technical difficulty of computing the couplings of the heavy and the light Higgs sectors, specifically the interaction (560 560) 320 involving the coupling of tensor-spinors with a third rank mixed tensor 320. An explicit analysis of such couplings is given in this paper. Spontaneous symmetry breaking of the SO(10) symmetry is carried out by reducing the gauge group to SU(3)c × SU(2)L × U(1)Y with just one pair of light Higgs. Thus a natural deduction of MSSM arises from the SO(10) model with no fine tuning needed. Further, it is shown that the light Higgs doublet of the model is a linear combination of the Higgs doublet fields of the 2×10 and the 320 Higgs fields. It is shown that in this class of SO(10) models b – t – τ unification can be achieved with tan β as low as 5–10. An analysis of the sparticle spectrum within ∼gSUGRA renormalization group evolution is given which leads to a bi-modal sparticle spectrum consisting of a compressed low mass spectrum for sleptons and weakinos and a high mass spectrum of gluino, squarks, and heavy Higgs. While the LSP is the light neutralino, the NLSP is found to be the light stau lying close to the LSP, while the remaining leptons, and the weakinos are also in close proximity to the LSP with masses in the few hundred GeV range. The cross section for slepton production and weakino production are estimated and appear promising for SUSY at the LHC. However, a more dedicated analysis is needed to predict the size of the supersymmetric signatures at the LHC.

The detection of a gravitational wave background in the nanohertz frequency range from pulsar timing array (PTA) observations offers new insights into evolution of the early Universe. In this work we analyze gravitational wave data from PPTA, EPTA, and NANOGrav, as arising from a supercooled first-order phase transition within a hidden sector, characterized by a broken U(1)X gauge symmetry. Several previous works have discussed challenges in producing observable PTA signal from supercooled phases transitions. We discuss these challenges and show how they are overcome by inclusion in part of the proper thermal history of the hidden and the visible sectors. The analysis of this work demonstrates that thermal histories of hidden and visible sectors profoundly influence the gravitational wave power spectrum, an aspect not previously explored in the literature. Further, the analysis of this work suggests that supercooled phase transitions not only align with the pulsar timing array observations but also show promise for gravitational wave detection by future gravitational wave detectors. Our analysis shows that the dominant contribution to the gravitational wave power spectrum for PTA signal comes from bubble collision while the sound wave and turbulence contributions are highly suppressed. It is also found that all of the PTA events are of detonation type while deflagration and hybrid events are absent. The analysis presented in this work provides a robust framework for further investigations on the origin of gravitational wave power spectrum in the early Universe and for their experimental observation in the future.

The Standard Model of cosmology, $\Lambda$CDM, while enormously successful, is currently unable to account for several cosmological anomalies the most prominent of which are in the measurements of the Hubble parameter and $S_8$. Additionally, the inclusion of the cosmological constant is theoretically unappealing. This has lead to extensions of the model such as the use of fluid equations for interacting dark matter and dark energy which, however, are ad hoc since they do not appear to arise from a Lagrangian. Recently, we have proposed $\mathcal{Q}_{\rm CDM}$ as an alternative to $\Lambda$CDM which is a dynamical model of a quintessence field interacting with dark matter within a field theoretic approach. In this approach, we analyze the effect of the dark matter mass, the dark matter-dark energy interaction strength and the dark matter self-interaction on the cosmological parameters. Further, within $\mathcal{Q}_{\rm CDM}$ we investigate the possible alleviation of the Hubble tension and the $S_8$ anomaly and the nature of dark energy.

The standard models of particle physics and of cosmology have been enormously successful in correlating a large amount of data. However, there are missing pieces and we are still far from what the ultimate model may look like. We give a broad perspective of both the achievements and of the missing pieces and discuss what may lie beyond.

The Standard Model of cosmology, ΛCDM, while enormously successful, is currently unable to account for several cosmological anomalies the most prominent of which are in the measurements of the Hubble parameter and S_8. Additionally, the inclusion of the cosmological constant is theoretically unappealing. This has lead to extensions of the model such as the use of fluid equations for interacting dark matter and dark energy which, however, are ad hoc since they do not appear to arise from a Lagrangian. Recently, we have proposed 𝒬_ CDM as an alternative to ΛCDM which is a dynamical model of a quintessence field interacting with dark matter within a field theoretic approach. In this approach, we analyze the effect of the dark matter mass, the dark matter-dark energy interaction strength and the dark matter self-interaction on the cosmological parameters. Further, within 𝒬_ CDM we investigate the possible alleviation of the Hubble tension and the S_8 anomaly and the nature of dark energy.

One of the important issues both in particle physics and cosmology relates to whether dark energy is a cosmological constant Lambda, or is dynamical in nature such as quintessence. In this work, we discuss a model of quintessence interacting with dark matter and analyze the resulting phenomenology of the dark energy equation of state. We identify two regions where the equation of state behaves differently depending on the size of the dark matter-dark energy interaction strength. We show that the strong coupling region induces a transmutation of quintessence from thawing to freezing. Using the recent data release from the Dark Energy Spectroscopic Instrument (DESI), we rule out this possibility of transmutation and investigate the weak coupling region to derive upper limits on the interaction strength. Our analysis indicates that while Lambda CDM lies within the 1 sigma contour in the w0-wa plane, the best fit points lie in the fourth quadrant and show deviations from the Lambda CDM prediction.

It is shown that the presence of an interaction between dark energy and dark matter can induce a transmutation of quintessence from thawing to scaling freezing. The analysis is done in a Lagrangian approach where dark energy and dark matter are treated as spin zero fields. Remarkably, with the cosmological constraints on energy densities of dark matter and dark energy, such a transmutation can occur in the late universe and searchable in accumulating cosmological data by DESI and other dark energy-related experiments. We give a fit to the dark energy equation of state which can be used by experimental collaborations to search for this transmutation that can occur at redshifts up to $z=13$ depending on the interaction strength. A transmutation in the range $z=1-3$ is already within reach of current and near future experiments.

While the standard model accurately describes data at the electroweak scale without the inclusion of gravity, beyond the standard model, physics is increasingly intertwined with gravitational phenomena and cosmology. Thus, the gravity-mediated breaking of supersymmetry in supergravity models leads to sparticle masses, which are gravitational in origin, observable at TeV scales and testable at the LHC, and supergravity also provides a candidate for dark matter, a possible framework for inflationary models and for models of dark energy. Further, extended supergravity models and string and D-brane models contain hidden sectors, some of which may be feebly coupled to the visible sector, resulting in heat exchange between the visible and hidden sectors. Because of the couplings between the sectors, both particle physics and cosmology are affected. The above implies that particle physics and cosmology are intrinsically intertwined in the resolution of essentially all of the cosmological phenomena, such as dark matter and dark energy, and in the resolution of cosmological puzzles, such as the Hubble tension and the EDGES anomaly. Here, we give a brief overview of the intertwining and its implications for the discovery of sparticles, as well as the resolution of cosmological anomalies and the identification of dark matter and dark energy as major challenges for the coming decades.

A variety of possibilities exist for dark matter aside from WIMPS, such as hidden sector dark matter. We discuss the synchronous thermal evolution of visible and hidden sectors and show that the density of thermal relics can change O(100%) and ∆Neff by a factor of up to 105 depending on whether the hidden sector was hot or cold at the reheat temperature. It is also shown that the approximation of using separate entropy conservation for the visible and hidden sectors is invalid even for a very feeble coupling between the two.

The description of dark matter as a pressure-less fluid and of dark energy as a cosmological constant, both minimally coupled to gravity, constitutes the basis of the concordance Lambda CDM model. However, the concordance model is based on using equations of motion directly for the fluids with constraints placed on their sources, and lacks an underlying Lagrangian. In this work, we propose a Lagrangian model of two spin zero fields describing dark energy and dark matter with an interaction term between the two along with self-interactions. We study the background evolution of the fields as well as their linear perturbations, suggesting an alternative to Lambda CDM with dark matter and dark energy being fundamental dynamical fields. The parameters of the model are extracted using a Bayesian inference tool based on multiple cosmological data sets which include those of Planck (with lensing), BAO, Pantheon, SH0ES, and WiggleZ. Using these data, we set constraints on the dark matter mass and the interaction strengths. Furthermore, we find that the model is able to alleviate the Hubble tension for some data sets while also resolving the S8 8 tension.

Production of gravitational waves in the early universe is discussed in a cosmologically consistent analysis within a first order phase transition involving a hidden sector feebly coupled with the visible sector. Each sector resides in its own heat bath leading to a potential dependent on two temperatures, and on two fields: one a standard model Higgs and the other a scalar arising from a hidden sector $U(1)$ gauge theory. A synchronous evolution of the hidden and visible sector temperatures is carried out from the reheat temperature down to the electroweak scale.The hydrodynamics of two-field phase transitions, one for the visible and the other for the hidden is discussed, which leads to separate tunneling temperatures, and different sound speeds for the two sectors. Gravitational waves emerging from the two sectors are computed and their imprint on the measured gravitational wave power spectrum vs frequency is analyzed in terms of bubble nucleation signature, i.e., detonation, deflagration, and hybrid. It is shown that the two-field model predicts gravitational waves accessible at several proposed gravitational wave detectors: LISA, DECIGO, BBO, Taiji and their discovery would probe specific regions of the hidden sector parameter space and may also shed light on the nature of bubble nucleation in the early universe. The analysis presented here indicates that the cosmologically preferred models are those where the tunneling in the visible sector precedes the tunneling in the hidden sector and the sound speed $c_s$ lies below its maximum, i.e., $c^2_s<\frac{1}{3}$. It is of interest to investigate if these features are universal and applicable to a wider class of cosmologically consistent models.

A variety of supergravity and string models involve hidden sectors where the hidden sectors may couple feebly with the visible sectors via a variety of portals. While the coupling of the hidden sector to the visible sector is feeble, its coupling to the inflaton is largely unknown. It could couple feebly or with the same strength as the visible sector, which would result in either a cold or a hot hidden sector at the end of reheating. These two possibilities could lead to significantly different outcomes for observables. We investigate the thermal evolution of the two sectors in a cosmologically consistent hidden sector dark matter model where the hidden sector and the visible sector are thermally coupled. Within this framework, we analyze several phenomena to illustrate their dependence on the initial conditions. These include the allowed parameter space of models, dark matter relic density, proton-dark matter cross section, effective massless neutrino species at big bang nucleosynthesis time, self-interacting dark matter cross section, where self-interaction occurs via exchange of dark photon, and Sommerfeld enhancement. Finally, fits to the velocity dependence of dark matter cross sections from galaxy scales to the scale of galaxy clusters is given. The analysis indicates significant effects of the initial conditions on the observables listed above. The analysis is carried out within the framework where dark matter is constituted of dark fermions, and the mediation between the visible and the hidden sector occurs via the exchange of dark photons. The techniques discussed here may have applications for a wider class of hidden sector models using different mediations between the visible and the hidden sectors to explore the impact of big bang initial conditions on observable physics.