Weakly dissipative quintessence explains DESI phantom crossing in dark energy without pathological dynamics.
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Modified gravity below O(10) Mpc in a CPL dynamical dark energy background is required to suppress structure growth at low redshifts while satisfying CMB constraints from ISW and lensing.
Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.
A two-field quintom model reproduces w0waCDM perturbation features and is mildly favored over it in Bayesian fits to BAO, CMB, and SNIa data.
Coupled quintessence-dark matter models can produce an apparent phantom-crossing effective equation of state matching DESI preferences if the scalar field begins frozen in the radiation era.
The paper derives the first law and checks the generalized second law of thermodynamics for linear, power-law, quadratic, exponential, and cross-coupling f(Q,T) models at the apparent horizon of a flat FLRW universe.
Quintessence models with standard potentials give only modest improvements over Lambda to DESI data on evolving dark energy, while non-minimal couplings allow temporary phantom behavior but face tight gravity constraints except for carefully selected narrow ranges.
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.