We know that dark energy is leading to the accelerating expansion of the universe and therefore determines the ultimate fate of our universe, but what other implications might it have on physics and our perception of it in our lives?
Assuming the dark energy is actually some new "stuff" with the ability to drive the accelerated expansion of the Universe, current theories for the nature of the dark energy could be grouped into two classes where the dark energy density:
If the dark energy is a Cosmological Constant, then either quantum field theories will need to be revised to explain the anomalously low value of the quantum vacuum energy implied by the observed dark energy density, or we may gain further understanding that we live in a "multiverse" with individual regions having different Cosmological Constant values. In this latter case, a common belief is that our value of the Cosmological Constant is then determined by anthropic arguments.
If the dark energy density evolves with time, then this implies the existence of a new particle, or quantum field, that must be incorporated in particle physics theories. In this case the dark energy equation of state and its time rate of change could potentially provide useful discriminating information between dark energy models, for example theories with extra dimensions of space or modifications to General Relativity.
If the apparent accelerating expansion of the Universe is due to a modification in General Relativity at large (i.e. cosmological) length scales then we may gain new understanding about the size and age of the Universe, as well as attempts to unify gravity and quantum mechanics. Finally it is also possible (although not considered very likely by the research community) that we are simply using the wrong solution to the General Relativistic field equations when using the homogeneous and isotropic Friedman-Lemaitre-Robertson-Walker (FLRW) solution to interpret the observations implying accelerated expansion (see the literature on "cosmological backreaction").
Any of these solutions to the puzzle of dark energy would be transformative for our physical understanding of the Universe, either in terms of its size, scope, or fundamental constituents.
Researchers are currently try lots of different ideas as to what dark energy could be, but there are basically three classes,
Modified Gravity Since gravity as already very weak, such theory would not make much difference on Earth like scales.
A Cosmological Constant from theory of the Vacuum. A promising example is QCD ghost dark energy. In such theories dark energy is a property of empty space and again would not make much difference to the rest of physics, or do much on Earth like scales.
Particle dark energy theories. E.g. Chameleons or Mass Varying Neutrinos. Another low mass particle, is present in the universe, it must be self interacting and hide itself somewhat in Earth scales, but it might have interesting properties, be observable in some conditions, or even interact with normal particles.