Approaches to Quantum Gravity

408 J. Hensonhistories suggest any measurable effects? Without the final dynamics any argumentswill have to be heuristic; but, when it comes to phenomenology, advancesare sometimes possible even before a full theory is defined [69]. Such considerationshave led in many interesting directions. One prediction is that no violation ofstandard, undeformed LLI (as opposed to the deformed Lorentz invariance of “doublyspecial relativity”) will be observed, as such an observation would undermineone of the major motivations for causal set theory. But this is a purely negativeprediction, so it is useful to search for something more.21.3.1 Predicting Perhaps the most significant phenomenological result for causal sets was the successfulprediction of the cosmological constant from a heuristic argument. Theargument is essentially a combination of unimodular (“volume-fixed”) QuantumGravity and the underlying random discreteness (see [2; 70; 71] for further details).From the classical theory, it can be seen that the spacetime volume V is conjugateto the cosmological constant , in the sense that position and momentum areconjugate in particle dynamics. But in causal set theory, there is an intrinsic uncertaintyin the volume of order ± √ V , where V is the past 4-volume of the universein fundamental units. V cannot therefore be fixed on a sharp value. Plugging thisuncertainty in V into the uncertainty relation, we can find the related “intrinsic”fluctuations in : ∼ 1V ∼ √ 1 , (21.2)Vusing fundamental units. If we assume that the value of the cosmological constant isdriven towards zero (taken as a natural assumption here), this equation tells us thatit could not be exactly zero in our theory, but will have fluctuations of order 10 −120(again in Planckian units) in the present epoch. This prediction was subsequentlyverified by observation.There are plenty of open questions surrounding this achievement. By this argument,the energy density in is, on average, comparable to the matter and radiationenergy density at all times. However, fluctuations in are to be expected, and in[70] these fluctuations are modelled. The hope is that this will lead to more detailedpredictions in cosmology. The path from theory to prediction in cosmology is typicallya tortuous one, and the introduction of a varying cosmological “constant”breaks the assumptions used in standard cosmology. Much effort will be requiredto modify the standard predictions in the light of this idea, and then compare themto observation.