Cosmological Data Suggest the Universe Will Never End in a Big Crunch

For decades, cosmologists have entertained a grim possibility: that dark energy, the mysterious force accelerating the expansion of the universe, might one day turn traitor. If the energy field driving that acceleration eventually dips into negative values, cosmic expansion could stall, reverse, and end in a catastrophic collapse known as the Big Crunch singularity. A new theoretical and observational study, published in The European Physical Journal C, argues that the data now weigh decisively against that apocalyptic scenario. By combining a sophisticated scalar field model of dark energy with the latest supernova, cosmic chronometer, and baryon acoustic oscillation measurements, the researchers show that observationally allowed versions of the model evolve toward a peaceful, eternal de Sitter state rather than a future collapse.

The work, carried out by Yerlan Myrzakulov of L. N. Gumilyov Eurasian National University in Astana, Saddam Hussain of Zhejiang University of Technology in Hangzhou, and Mohd Shahalam of Integral University in Lucknow, focuses on a class of models known as quintessence. In quintessence scenarios, dark energy is not the unchanging cosmological constant of the standard Lambda-CDM model but a dynamical scalar field that rolls down a potential energy landscape over cosmic time. The specific potential studied here is a double exponential, first proposed in the context of a recently introduced scenario called Quintessence-Driven Slow-Contraction Cold Dark Matter, or Q-SC-CDM. In that scenario, dark energy gradually loses strength, cosmic acceleration eventually ceases, and the universe drifts into a period of slow contraction that terminates in a Big Crunch.

The authors’ key innovation is to add a non-minimal coupling between the scalar field and gravity. In standard quintessence, the field interacts with gravity only through its energy and pressure. In the non-minimally coupled version, the field multiplies the Ricci scalar, the mathematical object that encodes spacetime curvature, through a coupling function of the form F(phi) = 1 minus kappa squared xi phi squared. The dimensionless parameter xi controls the strength of this coupling. When xi equals zero, ordinary minimal coupling is recovered; the value xi equal to one sixth corresponds to the theoretically motivated conformal coupling; and large values of xi can radically reshape cosmic evolution. This kind of coupling has a distinguished pedigree, tracing back to Brans-Dicke theory in 1961, and it has recently gained attention because a strongly coupled Higgs field can drive cosmic inflation.

Technically, the coupling changes everything. The Friedmann equation governing the expansion rate acquires extra terms proportional to xi, including contributions proportional to the Hubble parameter times the field and its derivative, and the field’s equation of motion picks up a curvature-driven term xi R phi. The researchers solved these coupled equations numerically on a spatially flat Friedmann-Lemaitre-Robertson-Walker background, starting from a matter-dominated early universe in which the field is frozen by Hubble damping. Their numerical experiments, sweeping the coupling across the range from 0.01 to 1 and varying the potential parameters alpha and beta, revealed a striking bifurcation. For couplings below roughly 0.2, and for sufficiently large potential parameters, the universe passes through decelerated expansion, then acceleration, and finally a slow-contraction phase in which the Hubble parameter falls to zero and the scale factor collapses. For couplings above roughly 0.2, the contraction phase vanishes entirely: the universe accelerates today and settles into de Sitter expansion, an exponentially expanding state with a constant Hubble rate, in the far future.

But a model that avoids the Big Crunch is worthless if it cannot reproduce the universe we actually observe. The crucial test is whether the model produces a sufficiently long matter-dominated epoch at high redshift, the era in which galaxies, clusters, and the cosmic microwave background patterns formed. The authors found that many parameter combinations producing a future slow-contraction phase fail this test badly: the matter era is cut short, the field’s fractional energy density turns negative or exceeds unity at high redshift, or the dynamics diverge. Such solutions, however dramatic their future, are physically non-viable. This observation alone begins to undermine the Q-SC-CDM picture, since the very trajectories that lead to a Big Crunch cannot sustain a consistent past.

To make the case quantitative, the team confronted three versions of the model with a formidable battery of data. The datasets included 32 cosmic chronometer measurements of the Hubble parameter spanning redshifts from 0.07 to nearly 2; the Pantheon+ compilation of 1701 Type Ia supernovae; the Dark Energy Survey five-year sample of 1829 supernovae; the Union 3 compilation of 2087 supernovae; and seven baryon acoustic oscillation data points from the second data release of the Dark Energy Spectroscopic Instrument, DESI, with the sound horizon at the drag epoch treated as a free parameter. Using Markov chain Monte Carlo sampling with the dynesty nested sampler, they computed posterior distributions and Bayesian evidence for each model relative to Lambda-CDM, interpreting evidence differences on the revised Jeffreys scale.

The results were unambiguous. Model I, with the coupling fixed at xi equal to 0.3, yields a Hubble constant near 70 kilometers per second per megaparsec and a matter density around 0.295, but its Bayesian evidence falls far below that of Lambda-CDM across every dataset combination. Model II, with xi equal to 0.5, fares even worse: it prefers a matter density of only about 0.255, produces a sound horizon near 145 megaparsecs, and shows the largest deviations in the Om(z) diagnostic, a low-redshift test that flags dynamical dark energy by measuring departures from constancy in a normalized combination of Hubble measurements. Both fixed-coupling models predict Hubble constants above 70 kilometers per second per megaparsec, which might superficially look like a route to easing the Hubble tension, but the authors caution that the severe evidence penalty means this should not be read as a genuine resolution of that conflict.

The most interesting case is Model III, in which the coupling is allowed to float between 0.01 and 0.7. Here the data consistently pull the coupling down to a small value, xi of roughly 0.12, close to the conformal value of one sixth. The best-fit evolution closely mimics Lambda-CDM: the matter density stays near unity at high redshift, the effective equation of state remains at zero through the matter era and saturates at minus one in the future, and the potential-related combination y squared minus A squared stays positive throughout, meaning the effective potential never turns negative. Because a negative potential is precisely what triggers recollapse in these models, the observationally favored parameter space simply never enters the Big Crunch regime. Even for this modest coupling, well below the threshold of 0.2 that mechanically eliminates contraction, the data steer the model into the corner of parameter space where the potential parameters are small enough that slow contraction never occurs.

An independent phase-space analysis confirms the picture. Rewriting the field equations as a first-order autonomous system, the authors identified five stationary points and classified them by the eigenvalues of the linearized flow. Points A1, A2, and A4 are saddle points corresponding to transient matter-dominated or non-accelerating phases; A3 is a non-hyperbolic point with de Sitter characteristics; and A5 is a one-parameter family of equilibrium points that acts as a stable attractor. For the observationally preferred parameters, with alpha near ten to the minus four, beta near 0.26, and xi near 0.12, the three transverse eigenvalues at A5 are negative, and phase portraits show trajectories from across the phase space converging onto the equilibrium curve. At that attractor, the field freezes, the Hubble derivative vanishes, the dark energy density parameter approaches one, and the effective equation of state approaches minus one, exactly the de Sitter endpoint implied by the observational fits.

The study leaves the standard cosmological model standing, at least at the level of background evolution: every variant considered was strongly disfavored relative to Lambda-CDM, with evidence differences exceeding five on the logarithmic scale. Yet the work delivers a substantive negative result with real physical content. The coupling strengths that would spare the universe a Big Crunch through brute force are ruled out by data, while the couplings the data prefer steer the universe away from collapse more subtly, by selecting potential shapes that never go negative. The framework also remains phantom-free, with a positive kinetic term that avoids ghost instabilities even as DESI measurements hint at evolving dark energy in other models. The authors note that the real test lies ahead: extending the analysis to cosmological perturbations, confronting the model with full cosmic microwave background data and large-scale structure surveys, and checking its impact on the matter clustering amplitude sigma eight. For now, the verdict is reassuring. The same observations that map the expansion history of the cosmos appear to be quietly vetoing the universe’s most dramatic possible ending, pointing instead toward a future of gentle, eternal expansion.

Subject of Research: Nonminimally coupled quintessence dark energy models and observational constraints on the future fate of the universe

Article Title: Nonminimally coupled quintessence with double exponential potential: observational evidence against big crunch singularity

Article References: Myrzakulov, Y., Hussain, S., & Shahalam, M. (2026). Nonminimally coupled quintessence with double exponential potential: observational evidence against big crunch singularity. The European Physical Journal C, 86(9), Article 1055. https://doi.org/10.1140/epjc/s10052-026-16306-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16306-7

Keywords: dark energy, quintessence, nonminimal coupling, Big Crunch singularity, de Sitter expansion, cosmology, scalar field, Bayesian evidence, DESI, supernovae, Lambda-CDM, phase-space analysis