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Here we generalize ideas of unified dark matterdark energy in the context of two measure theories and of dynamical space time theories. In two measure theories one uses metric independent volume elements and this allows one to construct unified dark matter-dark energy, where the cosmological constant appears as an integration constant associated with the equation of motion of the measure fields. The dynamical space-time theories generalize the two measure theories by introducing a vector field whose equation of motion guarantees the conservation of a certain Energy Momentum tensor, which may be related, but in general is not the same as the gravitational Energy Momentum tensor. We propose two formulations of this idea: (I) by demanding that this vector field be the gradient of a scalar, (II) by considering the dynamical space field appearing in another part of the action. Then the dynamical space time theory becomes a theory of Diffusive Unified dark energy and dark matter. These generalizations produce non-conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation of interacting DE-DM dust models in the form of a diffusive type interacting Unified dark energy and dark matter scenario. We solved analytically the theories for perturbative solution and asymptotic solution, and we show that the CDM is a fixed point of these theories at large times. Also a preliminary argument as regards the good behavior of the theory at the quantum level is proposed for both theories.

Baryon acoustic oscillations (BAO) involve measuring the spatial distribution of galaxies to determine the growth rate of cosmic structures. We derive constraints on cosmological parameters from 17 uncorrelated BAO measurements that were collected from 333 published data points in the effective redshift range 0.106 ≤ z ≤ 2.36. We test the correlation of the subset using a random covariance matrix. The Λ cold dark matter (ΛCDM) model fit yields the cosmological parameters Ωm = 0.261 ± 0.028 and ΩΛ = 0.733 ± 0.021. Combining the BAO data with the Cosmic Chronometers data, the Pantheon type Ia supernova, and the Hubble diagram of gamma-ray bursts and quasars, the Hubble constant yields 69.85 ± 1.27 km s−1 Mpc−1 and the sound horizon distance gives 146.1 ± 2.15 Mpc. Beyond the ΛCDM model we test ΩkCDM and wCDM. The spatial curvature is Ωk = −0.076 ± 0.012 and the dark energy equation of states is w = −0.989 ± 0.049. We perform the Akaike information criteria test to compare the three models, and see that ΛCDM scores best.

A unification of dark matter and dark energy based on a dynamical space time theory is suggested. By introducing a dynamical space time vector field χµ as a Lagrange multiplier, a conservation of an energy momentum tensor T µν (χ) is implemented. This Lagrangian generalizes the "Unified dark energy and dark matter from a scalar field different from quintessence" [Phys.RevD 81, 043520 (2010)] which did not consider a Lagrangian formulation. This generalization allows the solutions which were found previously, but in addition to that also non singular bouncing solutions that rapidly approach to the ΛCDM model. The dynamical time vector field exactly coincides with the cosmic time for the a ΛCDM solution and suffers a slight shift (advances slower) with respect to the cosmic time in the region close to the bounce for the bouncing non singular solutions. In addition we introduced some exponential potential which could enter into the T µν (χ) stress energy tensor or coupled directly to the measure √ −g, gives a possible interaction between DE and DM and could explain the coincidence problem.

From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.

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A mechanism of inflation from higher dimensions compactification is studied. An Early Universe capable of providing exponential growth for some dimensions and exponential contraction for others, giving therefore an explanation for the big size of the observed four dimensional Universe as well as the required smallness of the extra dimensions is obtained. The mechanism is formulated in the context of dynamical space time theory which produces a unified picture of dark energy, dark matter and can also provides a bounce for the volume of the universe. A negative vacuum energy puts an upper bound on the maximum volume and the bounce imposes a lower bound. So that in the early universe the volume oscillates, but in each oscillation the extra dimensions contract exponentially, and the ordinary dimension expand exponentially. The dynamical space time theory provides a natural way to exit from the inflation compactification epoch since the scalar field that drives the vacuum energy can smoothly climb into small positive values of vacuum energy, which is the end of the inflation compactification. A semi analytic solution for a step function potential is also studied, where all of these effects are shown. Especially the jump of the vacuum energy affect only on the derivative of dynamical space time vector field, and not the volume or it's derivatives, which match smoothly.