Editorial to the Special Issue “Origins and Natures of Inflation, Dark Matter and Dark Energy, 2nd Edition”

It has been confirmed from recent precise cosmological observations, such as Supernovae Ia (SNe Ia) [1,2], the cosmic microwave background (CMB) radiation [3,4,5,6,7,8], the large-scale structure (LSS) of the universe [9,10,11], the baryon acoustic oscillations (BAO) [12,13,14,15,16,17], and the weak lensing effect [18,19,20,21,22], that in addition to inflation in the early universe [23,24,25,26], even the current expansion of the universe is accelerating. Furthermore, it has been suggested from the Planck observations [7,8] that for the spatially flat universe, around 70% of the total energy density of the current universe is dark energy, around 25% of it is dark matter, and the rest is only around 5% baryons, which is well known. Not only have the identity of the inflaton field driving inflation, namely, the origin of inflation, been studied, but also that of dark matter and dark energy. Indeed, the true natures, i.e., the origins of inflation, dark matter, and dark energy, have not been determined yet.

Moreover, the Atacama Cosmology Telescope (ACT) [27,28], the South Pole Telescope (SPT) [29,30], and the DESI data [14,15,16,17] provide a new direction of observational constraints on inflation.

It is strongly expected that more fundamental and precise understandings of modern cosmology from the early universe to the present time can be found by future, observations including the Euclid satellite [31] of the European Space Agency (ESA) [32,33,34,35,36,37,38], the Roman Space Telescope [39], the Simons Observatory [40,41], and the James Webb Space Telescope [42,43].

In addition, by the direct detection of gravitational waves [44,45], the era of gravitational waves cosmology has been kicked off. It is expected that not only did the gravitational waves originate from astrophysical objects but also the primordial gravitational waves from the early universe, including the inflationary stage and cosmological first order phase transitions such as the Electro-Weak phase transition (EWPT) and the QCD phase transition (QCDPT) [46,47,48,49,50,51,52].

There are two representative approaches to account for the late-time cosmic acceleration. The first is to introduce unknown dark energy with negative pressure in general relativity. The second is to consider the deviation of gravitation from general relativity at cosmological scales, namely, the so-called geometrical dark energy. A number of candidates for dark energy and alternative theories of gravity have been proposed (for reviews, see, e.g., Refs. [53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92]).

There are also significant research themes in modern cosmology. For instance, physics in the early universe, including inflation [93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108], the cosmological perturbation theories [109,110,111,112], the picture of the Swampland related to a consistent quantum theory of gravity [113,114,115], the cosmological constant problem [116,117], cosmology through neutrino [118,119,120,121,122], cosmology through axion [123], primordial black holes [124,125,126,127,128], physics of dark matter [129,130,131,132,133,134,135,136,137,138,139,140], the origin of primordial magnetic fields [141,142,143,144,145], various aspects of big bang nucleosynthesis (BBN) [146,147], the Hubble tension [148,149,150,151,152,153,154,155,156,157,158], cosmology with a 21 cm hydrogen line [159,160], the effects of gravitational lensing [161,162,163], and the topics related to astrophysics [164,165,166,167,168,169,170,171].

In the present Special Issue “Origins and Natures of Inflation, Dark Matter and Dark Energy, 2nd Edition” of Universe, which is the second series of “Origins and Natures of Inflation, Dark Matter and Dark Energy” [172], fourteen original research papers, in terms of inflation, dark matter, and dark energy, are collected. The construction of this Special Issue is as follows. In the first part, a number of subjects in inflationary cosmology [173,174,175,176,177,178] are studied. In the second part, the various properties of dark matter [179,180,181,182] are explored. In the final part, the applied research on the issue of dark energy and alternative theories of gravity [183,184,185,186] is investigated. In the following, fourteen research papers are briefly overviewed.

In Ref. [173], the generation of cosmic strings in thermal inflation is driven by the so-called flaton, which is a complex scalar field with a very flat potential, and whose vacuum expectation value is a large one. The breaking scale of the symmetry in the present scenario is compared with that in the conventional Abelian Higgs strings.

In Ref. [174], the de Sitter swampland conjecture is studied in an inflation model motivated by the generalized Chaplygin gas model for dark energy, in which the Friedmann equation during inflation is modified from that in general relativity.

In Ref. [175], the Stueckelberg field is explored in de Sitter space. In particular, the regularization of the stress tensor is argued in detail for the case where the Stueckelberg field is a massive vector field with a specific gauge-fixing term.

In Ref. [176], the slow-roll inflation is explored in a gravity theory whose action is described by a kind of Einstein–Hilbert form with two parameters. In this model, the time scale of the slow-roll inflation with enough numbers of e-folds is altered by the quantum effect from that in the classical case.

In Ref. [177], inflation is investigated in a gravity theory with the Gauss–Bonnet invariant coupled to a charged scalar field. In particular, the mechanisms of the spontaneous symmetry breaking and that of the symmetry restoration are discussed.

In Ref. [178], k-inflation driven by a kinetic term of a scalar field is analyzed. In addition to the background dynamics of inflation, the properties of the perturbations generated during inflation are studied.

In Ref. [179], a geometrical origin of dark matter corresponding to a Proca field is argued in a gravity theory with the Weyl invariance. In particular, it is argued whether Weyl–Proca particles could behave as a gas in the Bose–Einstein condensate.

In Ref. [180], a new concept of a telescope through the gravitational lensing effect by Earth is proposed to detect distant sources of dark matter, such as axion-like particles. Especially, the structure of the focal region is analyzed numerically, and the sensitivity to the coupling of axion-like particles to photons is estimated.

In Ref. [181], the signatures of gravitational waves for warm dark matter are analyzed in the extended version of the standard model with the left–right symmetry, in which the type-II seesaw mechanism can be achieved for active neutrino masses, and the energy density of the keV sterile neutrino dark matter can be consistent with observations.

In Ref. [182], a laboratory search is explored for axion-like particles in the eV mass range through a photon collider with a variable-angle three-beam-stimulated resonance.

In Ref. [183], a K-essence model with two scalar fields is proposed to explain the late-time cosmic acceleration. In particular, the Lagrangian consists of the ratio of the two kinetic energies of the two scalar fields.

In Ref. [184], the transformation of energy from a dark energy component in its metastable state to the energy of a dark matter component is argued during a first-order phase transition.

In Ref. [185], a novel black hole solution is analyzed in $f\left(R\right)$ gravity, which is one of the promising candidates as an alternative theory of gravity to achieve cosmic acceleration, without supposing any non-linear electromagnetism nor a specific constraint on the scalar curvature.

In Ref. [186], a new black hole solution is studied in $f\left(R\right)$ gravity coupled to two scalar fields. The thermodynamics of a black hole and the stability of a black hole solution are also discussed.

It is strongly expected that these fourteen papers introduced above in this Special Issue are useful for the related future research on inflation, dark matter, dark energy, and other various aspects of modern cosmology.