What usually happens next
Dehydration is the most common reason.
Sugar or protein in the urine, or contrast dye from a recent scan, also raise it, so it's read with the glucose and protein lines on the same report.
When a urine specific gravity can read wrong
A first-morning sample is the most concentrated of the day. Glucose, protein and X-ray contrast in the urine push the number up without you being dehydrated.
Read it with
Nearby results

Questions
Is a urine specific gravity of 1.035 normal?
A urine specific gravity of 1.035 is above the usual 1.005 to 1.030. The usual range is 1.005 to 1.030.
Does a specific gravity of 1.035 mean I'm dehydrated?
Above about 1.025 urine is concentrated, which most often means you hadn't drunk much. Below 1.005 it's very dilute. In between is typical.
Worked out by LifeFrom from the usual urinalysis ranges (American Family Physician), and not yet reviewed by a clinician. For your own understanding: only a lab test, read by your clinician, diagnoses anything.