Ginzburg-Landau Theory of Dark Energy: A Framework to Study Both Temporal and Spatial Cosmological Tensions Simultaneously

A dark energy model (DE) is proposed based on Ginzburg-Landau theory of phase transition (GLT). This model, GLTofDE, surprisingly provides a framework to study not only temporal tensions in cosmology e.g. $H_0$ tension but also spatial anomalies of CMB e.g. the hemispherical power asymmetry and quadrupole-octopole alignment. In the mean field (or Landau) approximation of GLTofDE, there is a spontaneously symmetry breaking exactly like the Higgs potential. We modeled this transition, phenomenologically, and showed that GLTofDE can resolve both the $H_0$ tension and Lyman-$\alpha$ anomaly in a non-trivial way. According to $\chi^2$-analysis the transition happens at $z_t=0.738\pm0.028$ while $H_0=71.89\pm0.93$ km/s/Mpc and $\Omega^{like}_{k}=-0.225\pm0.049$ which are consistent with the latest $H(z)$ reconstructions. In addition, the GLTofDE proposes a framework to address the CMB anomalies when it is considered beyond the mean field approximation. In this regime existence of a long wavelength mode is a typical consequence which is named the Goldstone mode in the case of continuous symmetries. This mode, which is an automatic byproduct in GLTofDE, makes cosmological constant, direction dependent. This means one side of the sky should be colder than the other side in agreement with what has been already observed in CMB. In addition between initial stochastic pattern and the final state with one long wavelength mode, we can observe smaller patches or protrusions of the biggest remaining patch in the simulation. Our simulations show these protrusions are few in numbers and will be evolved according to Alan-Cahn mechanism. These protrusions can give an additional effect on CMB which is the existence of aligned quadrupole-octopole mode and its direction should be orthogonal to the dipole direction. We conclude that GLTofDE is a fertile framework both theoretically and phenomenologically.